Class 12th Mathematics Part I CBSE Solution
Exercise 2.1- sin^-1 (- 1/2) Find the principal values of the following:
- cos^-1 (root 3/2) Find the principal values of the following:
- cosec-1 (2) Find the principal values of the following:
- tan^-1 (- root 3) Find the principal values of the following:
- cos^-1 (- 1/2) Find the principal values of the following:
- tan-1 (-1) Find the principal values of the following:
- sec^-1 (2/root 3) Find the principal values of the following:
- cot^-1 (- root 3) Find the principal values of the following:
- cos^-1 (- 1/root 2) Find the principal values of the following:
- cosec^-1 (- root 2) Find the principal values of the following:
- Find the values of the following:
- cos^-1 (1/2) + 2sin^-1 (1/2) Find the values of the following:
- sin-1 x = y, then Find the values of the following:A. 0 ≤ y ≤ π B. - pi /2 less…
- tan^-1root 3-sec^-1 (-2) is equal to Find the values of the following:A. π B. -…
Exercise 2.2- 3sin^-1x = sin^-1 (3x-4x^3) , x in[- 1/2 , 1/2] Prove the following:…
- 3cos^-1x = cos^-1 (4x^3 - 3x) , x in[1/2 , 1] Prove the following:…
- tan^-1 2/11 + tan^-1 7/24 = tan^-1 1/2 Prove the following:
- 2tan^-1 1/2 + tan^-1 1/7 = tan^-1 31/17 Prove the following:
- tan^-1 root 1+x^2 -1/x , x not equal 0 Write the following functions in the…
- tan^-1 1/root x^2 - 1 , |x|1 Write the following functions in the simplest form:…
- Write the following functions in the simplest form:
- tan^-1 (cosx-sinx/cosx+sinx) , 0x pi Write the following functions in the…
- tan^-1 x/root a^2 -x^2 , |x|a Write the following functions in the simplest…
- tan^-1 (3a^3x-x^3/a^3 - 3ax^2) , a0 -a/root 3 x a/root 3 Write the following…
- tan^-1 [2cos (2sin^-1 1/2)] Find the values of each of the following:…
- cot (tan-1a + cot-1a) Find the values of each of the following:
- tan 1/2 [sin^-1 2x/1+x^2 + cos^-1 1-y^2/1+y^2] , |x|1 , y = 0 xy1 Find the…
- If sin (sin^-1 1/5 + cos^-1x) = 1 , then find the value of x Find the values of…
- tan^-1 x-1/x-2 + tan^-1 x+1/x+2 = pi /4 , then find the value of x. Find the…
- sin^-1 (sin 2 pi /3) Find the values of each of the expression
- tan^-1 (tan 3 pi /4) Find the values of each of the expression
- tan (sin^-1 3/5 +cot^-1 3/2) Find the values of each of the expression…
- cos^-1 (cos 7 pi /6) is equal to Find the values of each of the expressionA. 7…
- sin (pi /3 - sin^-1 (- 1/2)) is equal to Find the values of each of the…
- tan^-1root 3-cot^-1 (- root 3) is equal to Find the values of each of the…
Miscellaneous Exercise- cos^-1 (cos 13 pi /6) Find the value of the following:
- tan^-1 (tan 7 pi /6) Find the value of the following:
- Prove that
- sin^-1 8/17 + sin^-1 3/5 = tan^-1 77/36 Prove that
- cos^-1 4/5 + cos^-1 12/13 = cos^-1 33/65 Prove that
- cos^-1 12/13 + sin^-1 3/5 = sin^-1 56/65 Prove that
- tan^-1 63/16 = sin^-1 5/13 + cos^-1 3/5 Prove that
- tan^-1 1/5 + tan^-1 1/7 + tan^-1 1/3 + tan^-1 1/8 = pi /4 Prove that…
- tan^-1root x = 1/2 cos^-1 (1-x/1+x) , x in[0 , 1] Prove that
- cot^-1 (root 1+sinx+ root 1-sinx/root 1+sinx- root 1-sinx) = x/2 , x in (0 , pi…
- Prove that tan^-1 (root 1+x + root 1-x/root 1+x - root 1-x) = pi /4 - 1/2…
- 9 pi /8 - 9/4 sin^-1 1/3 = 9/4 sin^-1 2 root 2/3 Prove that
- 2tan^-1 (cosx) = tan^-1 (2cosecx) Solve the following equations:
- tan^-1 1-x/1+x = 1/2 tan^-1x , (x0) Solve the following equations:…
- sin (tan^-1x) , |x|1 is equal to Solve the following equations:A. x/root 1+x^2…
- sin^-1 (1-x) -2sin^-1x = pi /2 , then x is equal to Solve the following…
- tan^-1 (x/y) - tan^-1 x-y/x+y is equal to Solve the following equations:A. pi…
- sin^-1 (- 1/2) Find the principal values of the following:
- cos^-1 (root 3/2) Find the principal values of the following:
- cosec-1 (2) Find the principal values of the following:
- tan^-1 (- root 3) Find the principal values of the following:
- cos^-1 (- 1/2) Find the principal values of the following:
- tan-1 (-1) Find the principal values of the following:
- sec^-1 (2/root 3) Find the principal values of the following:
- cot^-1 (- root 3) Find the principal values of the following:
- cos^-1 (- 1/root 2) Find the principal values of the following:
- cosec^-1 (- root 2) Find the principal values of the following:
- Find the values of the following:
- cos^-1 (1/2) + 2sin^-1 (1/2) Find the values of the following:
- sin-1 x = y, then Find the values of the following:A. 0 ≤ y ≤ π B. - pi /2 less…
- tan^-1root 3-sec^-1 (-2) is equal to Find the values of the following:A. π B. -…
- 3sin^-1x = sin^-1 (3x-4x^3) , x in[- 1/2 , 1/2] Prove the following:…
- 3cos^-1x = cos^-1 (4x^3 - 3x) , x in[1/2 , 1] Prove the following:…
- tan^-1 2/11 + tan^-1 7/24 = tan^-1 1/2 Prove the following:
- 2tan^-1 1/2 + tan^-1 1/7 = tan^-1 31/17 Prove the following:
- tan^-1 root 1+x^2 -1/x , x not equal 0 Write the following functions in the…
- tan^-1 1/root x^2 - 1 , |x|1 Write the following functions in the simplest form:…
- Write the following functions in the simplest form:
- tan^-1 (cosx-sinx/cosx+sinx) , 0x pi Write the following functions in the…
- tan^-1 x/root a^2 -x^2 , |x|a Write the following functions in the simplest…
- tan^-1 (3a^3x-x^3/a^3 - 3ax^2) , a0 -a/root 3 x a/root 3 Write the following…
- tan^-1 [2cos (2sin^-1 1/2)] Find the values of each of the following:…
- cot (tan-1a + cot-1a) Find the values of each of the following:
- tan 1/2 [sin^-1 2x/1+x^2 + cos^-1 1-y^2/1+y^2] , |x|1 , y = 0 xy1 Find the…
- If sin (sin^-1 1/5 + cos^-1x) = 1 , then find the value of x Find the values of…
- tan^-1 x-1/x-2 + tan^-1 x+1/x+2 = pi /4 , then find the value of x. Find the…
- sin^-1 (sin 2 pi /3) Find the values of each of the expression
- tan^-1 (tan 3 pi /4) Find the values of each of the expression
- tan (sin^-1 3/5 +cot^-1 3/2) Find the values of each of the expression…
- cos^-1 (cos 7 pi /6) is equal to Find the values of each of the expressionA. 7…
- sin (pi /3 - sin^-1 (- 1/2)) is equal to Find the values of each of the…
- tan^-1root 3-cot^-1 (- root 3) is equal to Find the values of each of the…
- cos^-1 (cos 13 pi /6) Find the value of the following:
- tan^-1 (tan 7 pi /6) Find the value of the following:
- Prove that
- sin^-1 8/17 + sin^-1 3/5 = tan^-1 77/36 Prove that
- cos^-1 4/5 + cos^-1 12/13 = cos^-1 33/65 Prove that
- cos^-1 12/13 + sin^-1 3/5 = sin^-1 56/65 Prove that
- tan^-1 63/16 = sin^-1 5/13 + cos^-1 3/5 Prove that
- tan^-1 1/5 + tan^-1 1/7 + tan^-1 1/3 + tan^-1 1/8 = pi /4 Prove that…
- tan^-1root x = 1/2 cos^-1 (1-x/1+x) , x in[0 , 1] Prove that
- cot^-1 (root 1+sinx+ root 1-sinx/root 1+sinx- root 1-sinx) = x/2 , x in (0 , pi…
- Prove that tan^-1 (root 1+x + root 1-x/root 1+x - root 1-x) = pi /4 - 1/2…
- 9 pi /8 - 9/4 sin^-1 1/3 = 9/4 sin^-1 2 root 2/3 Prove that
- 2tan^-1 (cosx) = tan^-1 (2cosecx) Solve the following equations:
- tan^-1 1-x/1+x = 1/2 tan^-1x , (x0) Solve the following equations:…
- sin (tan^-1x) , |x|1 is equal to Solve the following equations:A. x/root 1+x^2…
- sin^-1 (1-x) -2sin^-1x = pi /2 , then x is equal to Solve the following…
- tan^-1 (x/y) - tan^-1 x-y/x+y is equal to Solve the following equations:A. pi…
Exercise 2.1
Question 1.Find the principal values of the following:
![](data:image/png;base64,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)
Answer:Let us take
= x
Therefore,
![](data:image/png;base64,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)
We know that principle value range of sin-1 is ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADwAAAAiCAMAAAA0/kqrAAAAAXNSR0IArs4c6QAAAFpQTFRFAAAAAAAAAAA6AGa2OgAAOgA6OmaQOma2OpDbZgAAZgA6ZjoAZrbbZrb/kDoAkLbbkNv/tmYAtmY6tmZmttv/25A627Zm29u22////7Zm/9uQ/9vb//+2///b2mNiqAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAA4klEQVRIS82V2RLCIAxFgztqW6tSRen//6ZQZEsZGGZcyFN7JrckhVwA/heCErI4Fa7fE0J2UiPoslA5pQtao1gcZFcymqAlj6bKvlz7Bhj+Gx5N9xwTA1j6PfHYqrKf93AbHU2uLGgDfLVBYkfr3Ofsia2kbDVkOqb5tG9B/R6tpOzs70UJJWWPLZqwn4nVoQ59IelhN+klW5t/PupHS9NTte9gmFmysDTb82Md83NNs2KmrHkWmubEg2vZ+8KbZsQsqjU0LeZSy9H+SGKoEUcvOnX/Yc9XnWpqLrrSQ/2p/Bc63xHZLaHbwgAAAABJRU5ErkJggg==)
And,
![](data:image/png;base64,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)
Therefore principle value of
is ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABkAAAAeCAMAAADuMkXpAAAAAXNSR0IArs4c6QAAAGBQTFRFAAAAAAAAAAA6ADqQAGa2OgAAOjo6OmaQOma2OpC2ZgAAZgA6ZjoAZjo6Zrb/kDoAkNv/tmYAtmY6tmZmttv/25A627Zm29u229vb2////7Zm/9uQ/9u2/9vb//+2///bGngKHgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAe0lEQVQ4T71SSRKAIAyrC4oL4K640P//UtQZL1YPOphbpzRpQwCcwuTeDnlRqZtSQhuS6i86qDa2RV/5TCphZDHRcXo5fdjhhoVf2Adn9f8mHxU7QRuKVXJj9M1XA6CKRUSyTYwPvaIiYjJrXxsQUqi4RnIGZptF/hSDFWNdBPqBe3hxAAAAAElFTkSuQmCC)
Question 2.Find the principal values of the following:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGUAAABFCAYAAABT0Cj5AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAASESURBVHja7Z29TuQwEIBTbUWPkDAdEpS7Zku602IhGjogWlFwokKWEPUpbLfSiRego6S4muJ4gn0DJHgD3uFu7eDEG+xsnIz3x5limqwUkvk8v56YaDQaRSirJagEhIKCUBDK6gmP2TFj8dX1eLyxrGcYj683YsauWMyPWw1FKOKCkod+zM/AVm8U/asq5gXSPyP04qHKAgkWCI3vT0BdSkMoQu5jeiLAtA6KAEIGN3fgfr5E2S5yMyB3854vKCByJRL27COGQEERlswIeS6z5KDclnhZxpOuDyBQUIQknHXLFk9QVhLRiycvKSowlNTNRk82awnHSrajV+jgDu26vi2ibfZqspYgoEh3EPUmwyTZWgSUhJ/v9kg0yTIu0puc82TX6ZmT4VYvIhOTu0XX5ei6xAKglP1WKzwHRD9cF4XNhQWSBtv9M6SVCDc5oINfRZeTWmr06foMtsWEWRdAPKkLxZaFrX88kb6593dR8cRmqXXcp+3ZEUqDVJjz866MJwfsT52CNVwocwoxH1aiUnC931W12VjF9SKUBq5LKFV2f6fxRIJx7LmtNZQ0kJI3UzBvAmWee6paNKpA75oWry0UmTZK5ZFPKChV2+0ulbwM9m2BMq/6beq+bGBcWyuiJW9rmyAUoCzLBYoK/O2KKWVQLvdOO53996nb2IRMf01QREuFRtFH2uviXaVYubFWYUfR8F6b+53O+95lcoqWUsGNmaAIAEd053EmFSYHLy5DEStvKWlwtOx1axXyIqCUxZdFt4jQUhzTZISyBCh1Mq/WQckLs3QFFzuxPiv6lYEiMowDQl6UEnbo0WPxhdOpv/5trizyaer9zATGacYy5MNDSuNkXdosKwFFrUo1WZitUq0oyppx2jXR/5GKLxRPIpCr3D1NHeu1uFsLJVN2QWkiB9fbB7JyNbQ80ut5U07EAZHT6+5GXkNLqQ6lyu6ZyUq++f6v3/L29hRgzTy+9VBU468Milr9RijqN82qMrcmYwp5gxy4bhWUsv5NGZTcMmY7pSJxmKmClxxTXAa1mwqY+yprP8+4pMKNMmAWpeuzUpCTJ+0I9F+rWX9JYUVKkcWAbotJpnGculMfrU6J8w0lXYg5JZ7+pmKEKXPL2tla/ZICdR9aazUU9ZL6SKYoHosjmapdrYPrs/hWV4z8gyy+4vzHYXa/GuOdCGUNBaEgFISCUBCKNYVX8RC6M4FQXO+pbRfoApnOIxQXRYlUnsWJ/g1KPqYKl9IjFIf70QH/6dLNQChLDPR1piARiu9MybDfhFCWCMXHx64IpbHrgj/vBaE0kCrnqSAUHYrnbx7ltoUhG/P57AhlXnoMPOjRCii+Ptm2nc0lJ++1ww18uN61h6LqB8ggrH/HaBKo+CI3/UI83ECtaqj6YWYCxyhwFX3Qx4CsY/s++ANzfB8t5c26Qz5aCtqFLTsOBgPF98E5i3S3wUDJ0tgVjy2tOtgzdwt+jsCFEtmymfMlcXBQfB0WDVb/VDhYJzgoOhgfU/6+gQQLJVcE/gMCFCBBJSAUlCryH6XJWekEdhvZAAAAAElFTkSuQmCC)
Answer:Let us take ![](data:image/png;base64,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)
Then, ![](data:image/png;base64,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)
We know that principle value range of cos-1 is [0, π]
And ![](data:image/png;base64,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)
Therefore, principle value of
is ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAeCAMAAADJnMQBAAAAAXNSR0IArs4c6QAAAF1QTFRFAAAAAAAAADqQAGa2OgAAOjo6OmaQOma2OpC2ZgAAZgA6ZjoAZjo6Zrb/kDoAkNv/tmYAtmY6tmZmttv/25A627Zm29u229vb2////7Zm/9uQ/9u2/9vb//+2///boQeaowAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAZ0lEQVQoU5VPSQ6AIBCriuACuCsu8P9nOoIHY4wJPTXtNNMCv7B14qHQD63CmPnrD+b05R4GsKXCyjixaIRfhOjkOzDJUMB1xV3krk6S5jL37sbEMutrkq0aYExJdFoY5zXstF08Z5xFRgSGcLOD0gAAAABJRU5ErkJggg==)
Question 3.Find the principal values of the following:
cosec–1 (2 )
Answer:Let cosec-1 2 = x
Therefore, ![](data:image/png;base64,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)
And ![](data:image/png;base64,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)
We know that principle value range of cosec-1 is ![](data:image/png;base64,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)
Therefore, principle value of cosec-1(2) is
.
Question 4.Find the principal values of the following:
![](data:image/png;base64,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)
Answer:Let us take ![](data:image/png;base64,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)
Then we get,
![](data:image/png;base64,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)
And ![](data:image/png;base64,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)
We know that principle value range of tan-1 is ![](data:image/png;base64,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)
Therefore, principle value of tan-1
is
.
Question 5.Find the principal values of the following:
![](data:image/png;base64,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)
Answer:Let us take ![](data:image/png;base64,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)
Then we will get,
![](data:image/png;base64,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)
And ![](data:image/png;base64,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)
We know that principle value range of cos-1 is [0, π]
Therefore principle value of cos-1
is ![](data:image/png;base64,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)
Question 6.Find the principal values of the following:
tan–1 (–1)
Answer:Let us take tan-1(-1) = x then we get,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
And ![](data:image/png;base64,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)
We know that principle value range of tan-1 is ![](data:image/png;base64,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)
Therefore, principle value of tan-1(-1) is ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABkAAAAeCAMAAADuMkXpAAAAAXNSR0IArs4c6QAAAF1QTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOjoAOmaQOma2ZgAAZjoAZjpmZrbbZrb/kDoAkDo6kGaQkNv/tmYAtmZmttv/tv//25A629uQ2////7Zm/9uQ/9vb//+2///b7gi28AAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAeElEQVQ4T2NgoCmQ5WYEAz4MW0REhfkYxFmx2k6GjBw/yDQZSUzzZLn4GKTYOLDI0NTn2D0GCQ0gYBICKoDz6O8SCm2UZsOMUbCRcgLsOGTEeYFRhA1IcYIiDwuQ5RGT4+cVxBJz4uCQY8EepzhMA1ogwcYshsfjAH9ZBLcoOFaeAAAAAElFTkSuQmCC)
Question 7.Find the principal values of the following:
![](data:image/png;base64,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)
Answer:Let ![](data:image/png;base64,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)
Then,
![](data:image/png;base64,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)
We know that range of the principle value branch of sec-1 is [0, π] ![](data:image/png;base64,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)
And ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAF0AAAAiCAMAAAAK2yXlAAAAAXNSR0IArs4c6QAAALFQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OjoAOjo6OjpmOjqQOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6Zma2ZpC2ZpDbZrbbZrb/kDoAkDo6kGYAkGY6kGZmkGaQkJCQkLbbkNv/tmYAtmY6tmZmtpBmtrbbttvbttv/tv//25A625Bm27Zm27aQ27a229u229vb2/+22////7Zm/9uQ/9u2/9vb//+2///bvrw7KwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACO0lEQVRIS91W13bCMAy100E6aYEOGrrTiaELO7X//8MqyZk9DgqnPFVPxthX0s2VZCH+s2XXr2V6ur9Yb6pm774GqPan64S3g4sGnNpmo/8YSdnvFkPaa55zyTFz0Q7vxDyqJ9x6wezgMQvRoGEaeqMDN/4aaz70x9f0QiifBR88HFJcggRl4pz1Cl0oPvh5N9pLpBp66bE1cdUNXKS5QlyCzHyTXOyASVsDuG4qLRiIHeSKQV3q+JDQXbJclHZQCID5qiYOhZnyxLNqwQOaNPjbVDcx+2vZRMoI+4cZyeiclALyjkjbf0ZHGt0lUGnisXhDBeIiowYQjlIFfYbJIAmYgwXpwyXwGQuhtKFXGaW+hMFayXqQ+y+l0AC5prgi9hKEAgzzRX+VB/MFbM135dYUZEw7G9Ma+t95R5dvca8qkhXQeWaQcqSaKPfVUjbdcNGvondSyAgAtRwLNwNJKlw8YgttqSZ2gKiCf5B7LCXV+CyW0Vm+2Lr7lUYluFpuYRVCx+4wAuBuJc4KKJxQ3ZE9bXPb3NeVjucnvomJ2l4LiAZ6Z7t54S9xVOrHPRwV0zqUTxNidi/cpMtwLZ4A+dijquNat7vxgfDDNcdyyeHJnmdm6ZPDPQEpxtOeXY1Z+j2YifufH1QHy0N/f4Ljfi6lcpNHF/QqsEOQPzriXgQ4Igs9UsNlzE2g97ukT8UMP5jjavsLicFw+PGOWO9QGxm+3hYie+aCscNbmkBYmrRYr600F1d2TV2xsB8UXjsFo6wj/AAAAABJRU5ErkJggg==)
Therefore principle value of
is ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAeCAMAAADJnMQBAAAAAXNSR0IArs4c6QAAAF1QTFRFAAAAAAAAADqQAGa2OgAAOjo6OmaQOma2OpC2ZgAAZgA6ZjoAZjo6Zrb/kDoAkNv/tmYAtmY6tmZmttv/25A627Zm29u229vb2////7Zm/9uQ/9u2/9vb//+2///boQeaowAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAZ0lEQVQoU5VPSQ6AIBCriuACuCsu8P9nOoIHY4wJPTXtNNMCv7B14qHQD63CmPnrD+b05R4GsKXCyjixaIRfhOjkOzDJUMB1xV3krk6S5jL37sbEMutrkq0aYExJdFoY5zXstF08Z5xFRgSGcLOD0gAAAABJRU5ErkJggg==)
Question 8.Find the principal values of the following:
![](data:image/png;base64,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)
Answer:Let us consider ![](data:image/png;base64,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)
Then we get,
![](data:image/png;base64,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)
We know that the range of the principal value branch of cot-1 is [0, π].
And, ![](data:image/png;base64,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)
Therefore, the principle value of
is
.
Question 9.Find the principal values of the following:
![](data:image/png;base64,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)
Answer:Let ![](data:image/png;base64,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)
Therefore,
![](data:image/png;base64,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)
We know that range of the principle value branch of cos-1 is [0, π]
And ![](data:image/png;base64,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)
Therefore principle value of
is ![](data:image/png;base64,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)
Question 10.Find the principal values of the following:
![](data:image/png;base64,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)
Answer:Let us take the values of ![](data:image/png;base64,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)
Then,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOIAAAAmCAMAAADut7dHAAAAAXNSR0IArs4c6QAAALRQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OgBmOjoAOjo6OjpmOjqQOmY6OmaQOma2OpDbZgAAZgA6ZgBmZjoAZjpmZjqQZmYAZmZmZpC2ZpDbZrbbZrb/kDoAkDo6kDpmkGYAkGY6kGZmkLbbkNv/tmYAtmY6tmZmtrbbttvbttv/tv//25A625Bm27Zm27aQ27a229u229v/2////7Zm/7aQ/9uQ/9u2/9vb//+2///b8Kaq7AAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAADJ0lEQVRoQ+1Z2XabMBCVvNGmcRvTprtxmta4C0rcxhSK/v+/OiMh4UVgKWDZPid6iDmg5c6dmTsDIeRpPDFwYgzwW1qOyYkh6wzOYp49T0gWTDvb8bgb5V9/7QLQJqZXq+PC6+D07MXcsEvlRXaZdHDKMbcoQmM0rgUqG565H+ORkeA1E3l03pqTPTOFKSFpv5IbvPY1mJJy+O3ozBonEiZMnPxFAjy6kc/MjLewtrYuxGAij3qfxN5or59RvOs87+3A+yuQqVkZ2vAbW6llEfoSnBjknS+vKR10FbBFaMUaj6yYaMO1XMtvICNi+pnkYVe5AYJihQsz08fIxpCKQgEZ7ah5TC03Yj0RNxlEUA+Oxt8xdn35DG5ghwd3pDSpKTGlwxVUADegTDPeiMwBB3EzMQswgqZQTOA3EpI7XPEvEMR4Z4lNu5oCvgBWeGRt4b8HJGihM7ApbpxwlN7ZG4MybJQ2iUhClRUyhMGFT3gEtyv5QvMrp4BTyyHjYWvktxT3LN6ofKg03LDSCYeticLbSlflr/i7oJc/1TWaty69WfDyqoG7Deh/HoTXdMlobDbccGgTt7ja7qIMJgqnkfsLOkjAXLGgn2xUF1v+BA9C+FgZ13LvurFp4j4cTrloYA9QLIOR9m91ga59+77S4T2Bik1iP9HdWzyqepzdlW44nExU3MoqidkiNR4kR7G+Rj/gtay60lsARWwHQ7y9pbXlzA2HbWcm9Y1BTebf54BmAopaCml+DUGV4pM7qBpqCuExQMSJtgOIu5ezxcuPWF8zXHDIDLAYpYbdBXTwDTMwoBSrYT6Di1dIPTzpfSwvcAqPaA+8SB1sZPRCpmIZmg3I7HEgEssGzmqaBVeNKnKYFqqpDa8U0dbZ7Wxkh+ExNVZimRKBftYwq51VPlbXvyYV4Qdtot0rlw+8jzmj9vNaPNG+q/lI95jjjrGmDn46XmkTz/0roxl/8RrKXxmoZ+5ELEMGIRNtMJiITaPH72+HCmM+2/2vRar68CmBx4c62eO+v81fLWSg5j88IvF91FlXQzuynN737LY8sVmQj/Wtz4lh7QjOf4H+bgqw59Q+AAAAAElFTkSuQmCC)
We know that range of the principle value branch of cosec-1 is ![](data:image/png;base64,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)
And ![](data:image/png;base64,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)
Therefore principle value of
is ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABkAAAAeCAMAAADuMkXpAAAAAXNSR0IArs4c6QAAAF1QTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOjoAOmaQOma2ZgAAZjoAZjpmZrbbZrb/kDoAkDo6kGaQkNv/tmYAtmZmttv/tv//25A629uQ2////7Zm/9uQ/9vb//+2///b7gi28AAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAeElEQVQ4T2NgoCmQ5WYEAz4MW0REhfkYxFmx2k6GjBw/yDQZSUzzZLn4GKTYOLDI0NTn2D0GCQ0gYBICKoDz6O8SCm2UZsOMUbCRcgLsOGTEeYFRhA1IcYIiDwuQ5RGT4+cVxBJz4uCQY8EepzhMA1ogwcYshsfjAH9ZBLcoOFaeAAAAAElFTkSuQmCC)
Question 11.Find the values of the following:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAaoAAAAzCAYAAADGkUzJAAAN0ElEQVR4Xu2dBcz9SBXFz+Lu7rq4u7u7s7i7Lw6B4AQWFndncZfFXYITnODuWbK4S37sbVK6r1+nfTN98/rOJP/sf/9fO23PPd+cmXvv3NlHbkbACBgBI2AEKkZgn4rfza9mBIyAETACRkAWKpPACBgBI2AEqkbAQlW1efxyO4zAWSUdIOkWkg7dYRz86ZtBoCr+Wag2QwI/1QisQuBWkvaVdBJJV5J0NEnnlHSI4TICMyBQLf8sVDNY348wAokInDdWTz+W9AZJF7dQJSLny3IgUC3/LFQ5zOs+jEB+BN5kocoPqntMRqAq/lmoku3mC43ArAhUNVDM+uV+WA0IVMW/pQvVGSV9X9J/arC832F2BLbZ/lUNFLNbbhkPNP8y2XGJQkUA+iyS7izpcpLOL+kvmfByN/UjsBT7W6jq59qqNzT/CthtaUJ1ckn3kPQ1SeeWdMP4r4WqAHkq7HJJ9rdQVUiwgVcy/wrZbGlC1YbpYZJuY6EqxJz6u912+1uo6ufYXm9o/mW0n4VKOkcI2oMl/SsR21NLurukx0r6Y+I9vmxeBFIHiin2n+NLUoXKXJzDGuOfYf6Nx6z3jl0XqotI2l/SHSX9biSuF4577zTh3pGP8uUTEEgZKNax/4RXGnVLqlDRqbk4CtpZLjb/MsK8y0J1ekmvknQDSb/owXSojAj3Xk/SbSX9I6Nd3NX6CAwNFCn2X/8tpvcwRqh4yi5z8ZiS3imJ1eVlJP1sOuzZ7jT/skGp3qK015D0BUm/zPisubvaiyhHkfRWSS+R9MbOi40pI3IESa+U9DlJT5vhA8koOlDSA+xyHER7qv0HO57pgrFCtctcpOTUtyUhWBeNsWsmM/U+xvzLaIG+FRXxGlYbP8n4rNSurivpPKkXx3WflPSBzj17EWU/SfeK2dffO/eNLSNCLbaDJV1KEqVvSrYTSvqgpCssuP7bpu1f0n5j+h4rVPS9y1y8tKTjS3r7mvsmzb/DWFoV/1YJFf/2LknEXjYhVNeXdK4xv9GSPiXpfYlCxWrqE5KeLenlA89JMRZ44XYgJf5BI9977OW7IFQ12X+sfXJe/44ooXR2Sb9K7NhcTARqj8vMv8PAqYp/q4TqgpI+IulsGxKq9al2WA99KyoKfSLEZHsN+bJThIpn3VzSIyRdoLBLbheEqib753qX1H5Y5Z9ZEnZmo/qRorLKN2KVAMf+MNCZuZiKdtnrcow/Zd/w8L1Xy7+2UB0rKjk8R9KpJDGz+HV8C8kGlCJqGvddXdJpIqX7FBHrYVXRbizFrymJnx87ztf5U/R9ovg3lPvrBSzSR5QnhR/7spL+PfDcVKGiVArfgEsON2SpNrdQHS8SRU4m6a8xSB7UE7vEnsT32Fx9xBhkXyHptx0w4M4V4ygLMi3hHfxigOb6rit2KpY57D/12Zu8b2lcHOILsTncdacM1x+ekiY5atvHn03yaOqzi/CvLVTM4HAzUHbodpLu3RpkmNF9Md4cYhDMZ1Xy1fi308b/QxKErmkMrNeOFQeDONUiGKReG2Q6X9xH1tx7piLTc98j49A5ntlUpuDdPybpy7EPauiRqUJ19AjgvkwSQliqzSlUxNyeJ4l4Ja5N6iXyi/94Sc+UBCeaduXgBGn+P4x/pIzVMwIP4mpNe3jgzwSlaWRqPVXSJTOWu8ph/1J2LNnv0rg4xBd4SQWam0m6Wowxzbi07eNPSZ6U6rsI/1a5/hhsXhCrpVUxKsSMgf51km7ZClySpk0GHO6vb3VQYCB7r6RHxcD159bPSUQgbsQ16xaPPYak+0lCkK4SLhQG2b9FkPWbIa5PiUF0yFipQkU/uEvJkrzpUKdr/HwuoWJWRNzvMSFKzSszc32LpKdLuk/8I5MNAthMQLp2JykGQWL1zWqbVRfZllzLCq3dnhj8WKfcVW77r2Gqjd66FC6O4QsT7A91hKo9kdrG8WejJFrj4dn5N0Wo2Kvw+VgBUaKoEZczSPperGLIGGw3MnI+Gq4hxKzdXhzixqbFXG6fPoxxaf4gVnivTzDEGKHiWoQEl2KpNpdQvUjSdSKLrB3IZxKCe+7RMVFhQoAQkTaP+HQnGrgAPy7pN+GewQXMbJfj1VmRtxsrbwYTJhWl2lj7l3oP+mXFl6Mx+eu2pXARd14qX5oxBg9Ks6JqcNnW8ScHP/r62Cr+TREqPpwgL+WGGJj4+wnCbfjhyBZ8YQedhii4eHC9tRtCxc/bLrpSBiJ9FxKz+mNmP9TGCBX7sXCBXkzSP4c67vk5sSBcrgjAqoYg3CREorsiaa7HJrjmhhJF+l6RmBErZgQKV9xecTxilLgAwRLxWdVYebOiYvM0fb5Z0rVixUY8j5UbWwt+PxGzMbeNtT99n07SXdS/53Do+UzqOK2320oOFEvhImNLKl9ShGrbxp9d5t///b5MFaojh4uLjcE/isGGmXCT1r6LQoWoMXCvI1RsXLxnuEKnChWr0udK+vnQCNrzc1bM7Adj0nH5gT4uEan+bJy+fc+1TESIeVKu6LOSjhs1Ekm8OE7cc6ik+0oixleyTREqbHq3NYSKjfMpq/ec370ULoJJKl+WKlS7yr9JQkXMgiA5qygywYhTMNMmHoNbh9YMcOy/qlWoxrp+xqyoluJuYVX3nUgOGXJj4q79TFT46BMq9qohSmyk/koM+HCHyQ6rLJ5BrJO9c6zgGNhLtbH2L/UepftdCheZSPMnhS/bIFTm30Tmp66oHhIlggh0M1tHoHDVtZMtukLFIMYMmlaL64/ZGa4/MsxSSh6lChU4EoNjFbPtyRQIyKclkZhATKqd+NLQjNgTkxZiZrj+KCHFNoRVjVU2XEGIcCsSy3pp58KjRqwLV+CqmMtEeh/utrH2z/XcOftZEhcZU1L5sg1CZf5N/E1YJVTMfpkFE29pSgJxGOHzY38MaersjYEY7fgF6e3MhpsVFfc8qzKhatLT2fPECcBDLVWoSMkEF9xcBwx1usbP50qmABtS09kcTQyp3eDM/SWROYn9+V5ifmT/deNMpLOzinp1VO1g4KFfRK2beIF7jesftwY+Q7eOtf9QfzX+fElcHMOXbRAq82/ib8wqocKPzwyZLKz3R7LEXSNAD9Cke1PVAWE6JJ7Lv5PWTpwBtx8rFv7Of2nsb2BmTcyD2Ee7kSFIIUlm3WwGLt3Y54SLiX1CQ+dPpZYROVOkX9Mn2JVqcwkVqyomK5xYSuJD+8wtRIZkkWbfG65gOEFCBKuhRoDgFnuuiNmRQcjmXgYeioeydaCdVMO1xLmY2JR0/WGXMfYvZceS/S6Ji2P4AqfgJBOmL3UA3tbxpyRPSvVdhH99tf6YMd849suQ9URWV1N1Aj8rAwoZaGzopO0r6TWxTGew4u9vi8oWzLgh3InDNYZ7jEMHGdQJsnPcArNAYmDsg2BwK9kYOKkLyH6wVfvEppQRoWzNQyVdqMdVlut75hIq3hd3HJt9iSGxQZsqJU2ssltxHpceWWwnlfTu+NirSvqppCe0hA4ekPrOSpW9c2QXNhVRyI6bI+lgyP65bDWlHyZ8bFwlO41YIdm0342K+d3Bt6//JXExhS/8ThCOaMYYJs+44QlXkN6+bePPFN7kuqda/u11HhUlj1BHflFW1RcjY4uMFDK2SIVuZtIMQLiEpqZo5wK9r5+mKC2uTFx167amEChxHTbIlmxzClXzHQgWAsV5W0wm9jp3q7mWe9lT190TBfb8YYVGDIxkClbRXDsXX3LbP5e9GSSY7CDeTSUQ3hWhxy3KBms4u1dbGhdr4Esu+zb9mH8TEF3ywYl7wcFqkTJQuADX3WBK8V7cmszUS5/ftQmhmkCr6m/Jaf9cH0uJMeLCuEDbjYGNFQIueVzke9XFNBdzWaNsP+bfSHx3VaiIwbCREFdTt1LGGAibw+qovkCSQOmGu5VSQ8y8V2XjlX7+UvrPZf+ceOASxc2Oy6ob59w/XFhPlvTAnoeaizmtUbYv828kvrsqVMBEbAyhYnZDWaUpjQrz/PFR9FPQ2+w9Oeyf8wtI3CFRhTqb3YzUpsYikyuOnF/VzMWc1ijfl/k3AuNdFipgYp8Qhx2SUk+sbUzjXma33EtGm9v2IbCO/XN/Le9yh0hQonhyu906qnZQZ5G/d5u5mNsa8/Rn/iXivOtCBUxkLJJ9yPlFQ+nqDaxkGJGyT4ZiO3U7EXZfVhECU+w/9+tTK5CjLFg1URWm3czFua2R93nmXwKeFqoEkHyJEdggAgxkxKzYd4ZQ7ZV1ucHX9KMXikAV/LNQLZRd/qxFIECpKqp6MFiwL6195MoiPtAfUTUC1fDPQlU1T/xyO44A1V0o2MsxKaW3Puw41P78FQhUwz8LlflpBOpEgBJmJFdwOCm1Nd2MwJwIVMU/C9WcpvezjEAaAmxE54BMMlLb++UoqWTRSsPQV01HoDr+WaimG9N3GoESCHAcyn5RO7GdOEGFCmpkHljioe7TCAQCVfLPQmV+GoF6EKAyBUemUPS5m91H3U0KBFPBws0IlECgWv5ZqEqY230agfEIcLrAwXHKwKr9fByncqMVx+SMf5LvMAKHR6Bq/lmoTFkjUAcCB0niiI6+RnV50tSnlvuq4yv9FrUiUDX/LFS10sbvZQSMgBEwAv9DwEJlIhgBI2AEjEDVCFioqjaPX84IGAEjYAQsVOaAETACRsAIVI2Ahapq8/jljIARMAJGwEJlDhgBI2AEjEDVCPwXLFpFcEOhQoYAAAAASUVORK5CYII=)
Answer:Let us consider tan-1(1) = x then we get
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIQAAAAmCAMAAAAyTsNwAAAAAXNSR0IArs4c6QAAAJNQTFRFAAAAAAAAAAA6AABmADo6ADqQAGa2OgAAOgA6OgBmOjoAOjpmOjqQOmY6OmaQOma2OpDbZgAAZgA6ZjoAZjo6ZjpmZmYAZmY6ZmZmZpDbZrb/kDoAkDo6kGY6kLyQkNv/tmYAtmY6tmZmttv/tv//25A625Bm27Zm27aQ2/+22////7Zm/7aQ/9uQ/9u2//+2///baTRcRwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABrUlEQVRYR+1Xa3OCMBDMYSt9C619QW2wldZCI/f/f10vIQKOJjC+wnS8DzGDYW+zt8kpY6dwrQBOQEfgjsqUi8sZE37kjoLMfCKx1P+kxFKJfNADY6aKRPDLXZ6PhEhg7L265PDfcs/H+yipuNgBZfEAVFhzdAXPve1JiLtPaXFzdASfylY2mOH3FcCIsRwg+vLljCIBOM9SemJJYyVhA1/BVGQxHmaYyJnwrzlLdV75BGNrn+ughAG8yaJWTLVVPZQ9HmNSomr3JIyORgWbJNYX2MDbSBShziz827IyxuighHq33qEGr3YEQC5Q28L52FfFV4srEixts20XEibwemeVJ9bJEpvHp9r925ZDemITeENdRUINa4oxfONFONy1HAbwJiz1MfbxTsPiWVYiL2uiPIEJfeRQOXMTG3u9LOCrYFPwIkYnevQTQiSkM4oQZGaMwSMl1Hxz4ISWw5mlDxrB7XY/6retvj8CG+G3Hb7DkyjCF/ckkqBjgzugHvlN5pxEcc/1dX3AjbZAYywvIY+nLv+M0i+XMlySUEI590RvSPThxiRfuL+t9AH6A9LNMVNo/dRTAAAAAElFTkSuQmCC)
We know that range of the principle value branch of tan-1 is ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADwAAAAiCAMAAAA0/kqrAAAAAXNSR0IArs4c6QAAAFpQTFRFAAAAAAAAAAA6AGa2OgAAOgA6OmaQOma2OpDbZgAAZgA6ZjoAZrbbZrb/kDoAkLbbkNv/tmYAtmY6tmZmttv/25A627Zm29u22////7Zm/9uQ/9vb//+2///b2mNiqAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAA4klEQVRIS82V2RLCIAxFgztqW6tSRen//6ZQZEsZGGZcyFN7JrckhVwA/heCErI4Fa7fE0J2UiPoslA5pQtao1gcZFcymqAlj6bKvlz7Bhj+Gx5N9xwTA1j6PfHYqrKf93AbHU2uLGgDfLVBYkfr3Ofsia2kbDVkOqb5tG9B/R6tpOzs70UJJWWPLZqwn4nVoQ59IelhN+klW5t/PupHS9NTte9gmFmysDTb82Md83NNs2KmrHkWmubEg2vZ+8KbZsQsqjU0LeZSy9H+SGKoEUcvOnX/Yc9XnWpqLrrSQ/2p/Bc63xHZLaHbwgAAAABJRU5ErkJggg==)
Therefore, ![](data:image/png;base64,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)
Let ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHgAAAAiCAMAAACjr+1xAAAAAXNSR0IArs4c6QAAAJZQTFRFAAAAAAAAAAA6AABmADpmADqQAGaQAGa2OgAAOgA6OjoAOjo6OjpmOjqQOmZmOmaQOma2OpCQOpDbZgAAZgA6ZjoAZjpmZrbbZrb/kDoAkDo6kGYAkGZmkLbbkNv/tmYAtmY6tmZmtrbbttvbttv/tv//25A625Bm27Zm27aQ27a229u22////7Zm/9uQ/9u2//+2///bJL+WVwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACIElEQVRYR+1X2VbCMBBNEKQqKFIRCmJxC6h0yf//nDNZypZJa1tePOaBcnqSmdx7Z25Sxv5HBQayp3dqVjLaVghQc0p680yvFIOPmmFLl+XhzDVHrvrqteidC3OsExyN9e1Ev5fRuHTvtSakVwTRwmwouTgP2W7AyLFJ3CpkKyBjaeBUeC8xE+1BLgQEXGRUi9iztxraFlFjqmhlfGnKOQ9bLC+bOA+dNQ1McBg6oYwadlQeYjDOUVSbOA0qoInbE7lInKhtlAzR8Vjbbm064bwD4fA5RBPO5vDi0HMLARsmlhHnvW0a8A72x5Rl4ILqGQFJKJFcHMi0E7ASGEHTovVPkBJbpsoYsEtVUaZDt+NWSryjJdZVAsOyr9oRK8bWvn6q3xUfvFEqFomPQprweplPD4Qm5wD4MLGMEPfmmncJv22oMfZanyVItwMxpP4MiHb9ZeJTqtH6YuwMjdF2PRKh5KUMirbqPXG8fZyH94+KTsGnTL48gzBjqGogQZW3OVxPpK5mIF7nio3BsXXAu0tUNuAcuzebw5874hphCfJZSMmcmuc1eUjsOZLfVhOifErsUPW+Y3yD741MN9GOCY2keqnGIM68/GHJNiahhxQZjRb1APtukeY2RtxCTe+Q1VNKAh1X6BPzbPdbKvBGS+wDXIrKP8F9zxQ6b6t3zKN9yLnjAymBvAn6vynthuCI5V8nR4i+Js1Y9nqejH8g6g9CYTAouNsDJQAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
We know that range of the principle value branch of cos-1 is [0, π]
Therefore, ![](data:image/png;base64,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)
Let ![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANEAAAAmCAMAAABtc458AAAAAXNSR0IArs4c6QAAAJZQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OgBmOjoAOjo6OjpmOjqQOmaQOma2OpC2OpDbZgAAZjoAZpDbZrbbZrb/kDoAkDo6kGYAkGY6kGZmkLaQkLbbkNv/tmYAtmY6trbbttvbttv/tv//25A625Bm27Zm27aQ27a229v/2////7Zm/7aQ/9uQ/9u2//+2///bjfwQ8wAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACx0lEQVRoQ+1Ya3ObMBCUnDQ0rVs3Tlq7L+O0oWliKsz//3OVxEsgHVpAMJOZ8MHjse9Wu3enOyHGXp/XCMgI5N94+dyEi8csoCi940FcPzARfUEdELtZQJGFC5upirLvv+3FatB0c8KpBLKcqEi8PziINKDJ+iEQURhmmqLz1lmvBmjyZuksTVMUXzlDZ4Dmu4A9B8pTejGhM4i3rppjzARV3xd9Eq3o5p+bmocKkSJmgi6epFgqyneruzFhJLt+C1TJeykPxjXwtJs1ODHUx85bqzekPNRIn4Jk+5637k7XiWK+s4RP4dFGn4Jk+8qGApWA2lUv40Hjk6yqRprtOV9tTimXVac+/kR8U5zFIn1gxiKkHEgkIHS072BFqv7yr7IGdbMQ0frAkmJHqR8c1UnSo5H8inp8m9j3w5SsGdM9QnyoFWlZOi/qxwYurl5xeJ3dzgo0UpeKjdXjiypqcnnk619VSopENY3Q0RIbdhYvEqkOBudUnGkWtaLOel1Qozof3/FL2SbKqmspGtg/epC8hUf6Dt5Haqm/kWz5DkUmmL/q+pDagtxYBIvBitRuYWos24r0bEvgXteD5M1Qjy96vKnrSUSfWXYrqetY6I9qphUnQVwRjeRXRPvCE7Y6M2R7OXY+qhTJWaQ/zttiCMnhNGge0UheQXKUUSxkTMFTEGTmpwJb5McIOnHagD0nVQMUTSVM2GeYRptnnw3xf0oNQGaC0lYjl/W4pXKfjH3IodgCxd45xnKw/MA3AmI94qKnBUpcFwVT0AVCZ4qbAMG2Bbr09VZ88eOW89E3n266JujSKcp3/NNJnkzg0WYdbR2d2QQdMDXD1GH5TjJ+8+Z7O78GqPw7DFEYpVwcu9Rxoz5Zr9wGaHYPUwllWJy5xufIyWMWUFSxiK5O7DHYZVOx7CygqCImZKu7/AmbY4azgGJLL2r1H3ylWEI7yHnEAAAAAElFTkSuQmCC)
We know that range of the principle value branch of sin-1 is ![](data:image/png;base64,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)
Therefore ![](data:image/png;base64,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)
Now,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 12.Find the values of the following:
![](data:image/png;base64,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)
Answer:Let ![](data:image/png;base64,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)
Then, we get,
![](data:image/png;base64,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)
We know that range of the principle value branch of cos-1 is [0, π]
Therefore ![](data:image/png;base64,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)
Let ![](data:image/png;base64,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)
We know that range of the principle value branch of sin-1 is ![](data:image/png;base64,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)
Therefore ![](data:image/png;base64,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)
Now,
![](data:image/png;base64,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)
Question 13.Find the values of the following:
sin–1 x = y, then
A. 0 ≤ y ≤ π
B. ![](data:image/png;base64,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)
C. 0 < y < π
D. ![](data:image/png;base64,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)
Answer:sin–1 x = y
We know that range of the principle value branch of sin-1 is ![](data:image/png;base64,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)
Therefore,![](data:image/png;base64,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)
Hence, the option (B) is correct.
Question 14.Find the values of the following:
is equal to
A. π
B. ![](data:image/png;base64,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)
C. ![](data:image/png;base64,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)
D. ![](data:image/png;base64,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)
Answer:Let us take
Then we get,
![](data:image/png;base64,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)
We know that range of the principle value branch of tan-1 is ![](data:image/png;base64,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)
Therefore, ![](data:image/png;base64,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)
Let
Then we get,
![](data:image/png;base64,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)
We know that range of the principle value branch of sec-1 is [0, π] ![](data:image/png;base64,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)
Therefore, ![](data:image/png;base64,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)
Now,
![](data:image/png;base64,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)
Hence, the option (B) is correct.
Find the principal values of the following:
Answer:
Let us take = x
Therefore,
We know that principle value range of sin-1 is
And,
Therefore principle value of is
Question 2.
Find the principal values of the following:
Answer:
Let us take
Then,
We know that principle value range of cos-1 is [0, π]
And
Therefore, principle value of is
Question 3.
Find the principal values of the following:
cosec–1 (2 )
Answer:
Let cosec-1 2 = x
Therefore,
And
We know that principle value range of cosec-1 is
Therefore, principle value of cosec-1(2) is .
Question 4.
Find the principal values of the following:
Answer:
Let us take
Then we get,
And
We know that principle value range of tan-1 is
Therefore, principle value of tan-1 is
.
Question 5.
Find the principal values of the following:
Answer:
Let us take
Then we will get,
And
We know that principle value range of cos-1 is [0, π]
Therefore principle value of cos-1is
Question 6.
Find the principal values of the following:
tan–1 (–1)
Answer:
Let us take tan-1(-1) = x then we get,
And
We know that principle value range of tan-1 is
Therefore, principle value of tan-1(-1) is
Question 7.
Find the principal values of the following:
Answer:
Let
Then,
We know that range of the principle value branch of sec-1 is [0, π]
And
Therefore principle value of is
Question 8.
Find the principal values of the following:
Answer:
Let us consider
Then we get,
We know that the range of the principal value branch of cot-1 is [0, π].
And,
Therefore, the principle value of is
.
Question 9.
Find the principal values of the following:
Answer:
Let
Therefore,
We know that range of the principle value branch of cos-1 is [0, π]
And
Therefore principle value of is
Question 10.
Find the principal values of the following:
Answer:
Let us take the values of
Then,
We know that range of the principle value branch of cosec-1 is
And
Therefore principle value of is
Question 11.
Find the values of the following:
Answer:
Let us consider tan-1(1) = x then we get
We know that range of the principle value branch of tan-1 is
Therefore,
Let
We know that range of the principle value branch of cos-1 is [0, π]
Therefore,
Let
We know that range of the principle value branch of sin-1 is
Therefore
Now,
Question 12.
Find the values of the following:
Answer:
Let
Then, we get,
We know that range of the principle value branch of cos-1 is [0, π]
Therefore
Let
We know that range of the principle value branch of sin-1 is
Therefore
Now,
Question 13.
Find the values of the following:
sin–1 x = y, then
A. 0 ≤ y ≤ π
B.
C. 0 < y < π
D.
Answer:
sin–1 x = y
We know that range of the principle value branch of sin-1 is
Therefore,
Hence, the option (B) is correct.
Question 14.
Find the values of the following: is equal to
A. π
B.
C.
D.
Answer:
Let us take
Then we get,
We know that range of the principle value branch of tan-1 is
Therefore,
Let Then we get,
We know that range of the principle value branch of sec-1 is [0, π]
Therefore,
Now,
Hence, the option (B) is correct.
Exercise 2.2
Question 1.Prove the following:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAWgAAAA7CAMAAABhVuAKAAAAAXNSR0ICQMB9xQAAAM9QTFRFgYGBiIhmZoiIboBugG5ubm6Af39dXX9/f25ZWW5/f39AQH9/f25Ibm5ZWW5uSG5/bm5EXW5dbltISFtugFszM1uAbls1NVtuW0hISEhbM0ZuW0g1bEYdHUZsRkYzRjNGWzMzHUhbMzNbSDMzMzNIbTMLWjMdHTNaRzMeHjNHWjMAADNaNDQdNB00SB0dHR1IADRINB0dHR00AB1OMgAySBwAABxIHBwcMh0AAB0yMgAdHQAyHR0AAB0dHQAdMwAAAAAzFAAUHQAAAAAdAAAAXf+IcwAAAER0Uk5TAAwMGBgYGRklJSoqMTExMT09SkpMTFhYY2NkcXNzfX1/f3+Li42NjZqaoaGoqKmprbe3uLu8vMXKysrK2dnZ3d3l7Oxr29jbAAAEnElEQVR42u2ca3uTMBTHE5yUKbO60k4rqKuzraDOG7XTzc423/8z+RAuDZBAAsTRec6rPech/5P8SE4upEMIDAwMDAzsIM3ckMh2w0alXVqYeMCxHvT3QWsNF0AD6MMAffLq2pNwA+iWoJ2ba176LbkBdOvU4fDnOQdAA2gADaDvL2hrpFH8dACg07ZdGDrVPw4OA7T9e6ij/YzsXEcAh5Ag+WtxEKCdptt+aVk1ELK8ZsjcjJMXOT6IHm3+1NKjM1kcjjXIHxkI+YmwszIANELO7QBpMTdo0oL7C9oPtGDGYZqjEQ6D7kAHEu5K0HNRKm4FWqiayZobXWshe5squwqDpgq0veUeNpfcDGhrTcjVcQWSuHA0Y3UKuixrb8fCOimkCR7KLHc4CvN5t8ek9oWBrLXce9acOtwUgkqdyn2KV84JSn37H4PGr41cX7pL0H4CWqlORa014YDGn4YZ6OCOenRh0FZ3FkI0rL9SWRzmEDUDPT8Pi6Bd9rOfuZFf4GkAHU33eEmuns2iBLn8PUT45fX4dE0WpVrRL5aeuZHdvKSy1aqxcg6RHyjHinY89HWJC7JBOE/h+Xb/PbYL0A47gE7Wn6M1vYdwBNymgX1C3o+Qy+nB2CcrAzm3knNVIlunWuxscZ0UY0WHGfG4EBbMvc3SU9aXM6PbHs2AxiEhZGHQXao5o47ohVIa3KkDh2S8T3rsCE3NYxuWyNapRu4MdFInYSxh4himCUhUMK6GoCmFAp33aDzZEg+Hu/SE0meQBPwx/kE2f+5l61RZ0EmdFGPRhJhmekHBPOjCU/YCaQUdr4kmhNycySFxiPyMksmqgc7WaZxYyQq8dLmFcsqmVH4lC6DzT7l52T1o/mhtABr5twNkLZPjxHrQPxTipbKqoGmdlGJlOCoKlkCzTxWoCHs0Ya3aXQTt0jZaazpN1SGxLx+EO8kcjTLZWtCFVUdcJ36sylwVqwgKFteQuafsXwPNqQOHHt0lxGvXGiTRdwr+/ovX7kxWFTQOPcVYLElRwXyQwlM0pCbQ1ubqCcLzBcLhwojPCcwN7YBRv+Tlubg2Llkdy7U7ka1RZTtbVifFWIyKsCBdQ+JwN+U2xd4uHqqDTuUqQeMlIeTrCCH84umaHuTQqeY8Wl95UTYoMfGj1ODK3rJMZetUc1vwtE6KsRjQwoJ0NJlhnMbLTx012bCkcjKTYS/M1fKljH9g+kaC4aM/j2VlhXLvvvUQdLPTDcWcGb9Me4q6BC2W6yVofQf/hdNq/Fzq9ogs6Cq5XoJG/srQHkIhZ1aBpp8mRvXufoIurGO1DJpxJ6CTzem41t1P0HquG+RStMqYEYPG4bmBrNJig+PuJ2jkXGrOHUoXaMSg7SlvO89z9xS0GogGuUnpJlTtZOjzl89+/3u06jVE1dT0dtAlaMElkZy7r6CRqfXartoNhjrQgrk75+4t6D5ZHWhBnsu5AbTM6Ko+6xDc9nLhpxXdgnamMm4A3Ra0PZNyA+iWoOMr81bxlyAlN4BuB3qy5X60K7sBdCvQE95HeK4bQLdfdUgZgAbQAPr/Aw3/6gcMDOwu7S9A+QlWL8YbLAAAAABJRU5ErkJggg==)
Answer:Let ![](data:image/png;base64,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)
We have,
R.H.S =![](data:image/png;base64,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)
Now, we know that,
sin 3x = 3sin x - 4 sin3x
Therefore,
= sin-1(sin (3θ))
= 3 θ
= 3sin-1x
= L.H.S
Hence Proved
Question 2.Prove the following:
![](data:image/png;base64,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)
Answer:Let x = cos θ
Then, Cos-1 = θ
Now, R.H.S. = cos-1(4x3 - 3x)
= cos-1(4cos3θ - 3cos θ)
= cos-1(cos3θ)
= 3θ
= 3cos-1x
= L.H.S.![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAQAAAAXAgMAAABR3QbYAAAAAXNSR0IArs4c6QAAAAxQTFRFAAAAAGa2ZgAA//+2sdvXUQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAEUlEQVQYV2NgIACeMDxBqAAAFY4ByRSePcMAAAAASUVORK5CYII=)
Hence Proved
Question 3.Prove the following:
![](data:image/png;base64,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)
Answer:L.H.S. ![](data:image/png;base64,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)
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![](data:image/png;base64,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)
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![](data:image/png;base64,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)
= R.H.S.
Hence Proved.
Question 4.Prove the following:
![](data:image/png;base64,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)
Answer:L.H.S. = ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHcAAABJCAMAAAAwl0llAAAAAXNSR0IArs4c6QAAAJNQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OjoAOjpmOjqQOmZmOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZmY6ZmZmZpDbZrbbZrb/kDoAkGY6kLyQkLbbkNv/tmYAtmY6tmZmttv/tv//25A625Bm27Zm27aQ2/+22////7Zm/9uQ/9u2//+2///bk0rNrgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAC2UlEQVRoQ+1Y7VLbMBCUDG1xaZsQN1CwKVEKhhB/6P2frrqzZSuxpUj1kZnOWD+Mhyjau72TdhXG5vG/MCB3a84/bSDct2vOo3tb4BI+biZSDMEfWJVcvDCWRw8Km6+6VWWWGggiemJVFlEBiyu1ds5TJjN4Y+LzXoMd4eqJFNm2axQGLqLjOMTFfwkghm7gcoVinL0ZRA5wq8fFMx0oY2WMhdzFqq+M+h3h1gnni64IBPgyw14qY/UHKo2Ecj3MSHYxIc9tQ8kMOqp5WutbGO0+NWNxhUh10vRzn9FIXyEnNCOHBIuVztS2j5piQOPTjPKr6iQpsLQ3e/u5IeHIqIwqTIRvGwiSwYPwqV/vkOfqUbX7krKfJ0Y+f31mYMBAdxz6v8wsEjBg2C0ljLeGKhIs7liit1usWnNC1TsRdme3WLl4zs+Hi2Fp1Tk3rtZgaly57U3jCO+t3VLKSMvz64+1C7e1WyogYly1oAO3tVvAw1lxW7sViou+ZWSA+4WB/siRr7ZbobiFz83JjtvbLQjPZ60mxy3kdPGCl8Yl7ESevsbwZg4pvth8Um+3JPgpfmm9lx5xivmq3thLAW9l/G3TXQLaqTnENs0HD68TPc+4DdvHNBQfSRjDrRMLrr/YH8wci6PBlbtbVR2drxXXJ5HRORaeob6aYgVOjzsMBvPFR19fF26Q0Ds2FtzY/vxWj+oO+golzXWLCxH6MnZs6C2PUtjGy/eEpyVUGY4qa0MHCH2d/PI/SLxax0/oxcrrMPRCbCZ5CX3xfU+M6yX09c9N069kY0zoBxsUJyncnOrCr3+ogzQcQq8UxhBSipwDhJ6S5xChJ8QNEvoAI3CqEiFCr2pM2tCnYps/nxkIZOAfHFYgwjx9jIEgu0VIYYjdIoRlAXaLErZZy89u0eN62S16WC+7RQ/7gb+ruIL9yN9VXLgBdouS6xC7RYgbZLcIcUPsFiGs31J/Aa4ZSggaW47nAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
= R.H.S.
Hence Proved.
Question 5.Write the following functions in the simplest form:
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
Now, Put x = tanθ ⇒ θ =tan-1x
Therefore, ![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJMAAAArCAMAAABLoko/AAAAAXNSR0IArs4c6QAAAJxQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OjoAOjpmOjqQOmZmOmaQOma2OpC2OpDbZgAAZjoAZjo6ZmY6ZpC2ZpDbZrbbZrb/kDoAkDo6kGYAkGY6kGZmkLyQkLbbkNv/tmYAtmY6tmZmttvbttv/tv//25A625Bm27Zm27aQ2/+22////7Zm/9uQ/9u2//+2///bcb0G9gAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAC90lEQVRYR+1YYXPaMAy1w9qRrVvZQrc1dO1G6EoYgwT///82SY4dGiyHBJNr76oPOR849ov09GRZiDd7MR5Q91JONi8GDgJRs/GmTMY8pvXNfGjA2wi2pIfTyqkcLc+AST088atmlxC3Ik7dM4rrp1xjKiZBkS2+ClHeSRkhbYqpjH7QJlP4JYXQwXiXwBTGKkwCVwlmOeyqZpcb9RNcUsS3Yo1ewUGZVJg0MrcZTGrG+LIH0OIDcIUcUXzaCAwVIaCY4R+SrB2T2IYjVkbbLeTVHxskwGOitaOUM37KNECwmvTGTzApVPTITWB/P8qLpXHLaGkwHc8nyM5Qjsp1jMDW8bgms2U1xXCX8FyxfvJmQhdSVXsjlZBClsx2kJM+eTxQYzIc7LK/a26lhpRlU6DOVt4KtQIxyHHwOIePRx33MIVAa+OltR2mWtg0qr6yvIulvMYormIZfa8GF7/hB1Dq6Au3prqH9+Q7EjTUj94sX31Gj5ChLrV/w7EzfDLWugbKJJlO9WBWiVqv9SymE7zt2jhz54LRm+YrRpApqS2mrQxXEHBd9/nhKO4Pi2mBwj9aKpBlOcHUlilkEoz2TWXvK2YzH9aLEPAS43byEx4OVYajIr6ag9Y8i1COuHXWngPTYVGsY0cHserB6cY5MB062YWJP5IZTLbe9x4QEl/shFrfgMAaP7Vj6kugxnuEiYkd8smEDWYNi4mJHQWw5hOPaRh9QmV+/AWP8htynDbl1XoYTHCKjVJ4yMm/RKYFsgolnEm87rXF2xYztaUbWzvXYH9bfEoNtsC5swpXNfWxjatfJ51VamfunVz3PcxWTW9b3J0Jzqi6N2erpr+NOar+t5OLkQmuampMXIyC0AmrsPPwy1VNb1vsu1Vo987eDDebuar5vC1uVpZQPafQvXlzeTowHlZNH5/C9ebC6SjLp2aF8rTFwVpzZJTDUbUMNaom3xaHvOuBO5XDwsNWTb4tDnonJlx3h2zV5NriwHeHnfL0NU7+D6NQWyVEze8lAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Therefore, ![](data:image/png;base64,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)
Question 6.Write the following functions in the simplest form:
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJMAAAAgCAMAAAAhZbr8AAAAAXNSR0IArs4c6QAAALpQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OjoAOjpmOjqQOmY6OmZmOmaQOma2OpDbZgAAZgA6ZgBmZjoAZjo6ZjpmZmYAZmY6ZmaQZma2ZpC2ZpDbZrbbZrb/kDoAkDo6kGY6kGaQkJCQkLyQkLbbkLb/kNv/tmYAtmY6tmZmtpBmttv/tv//25A625Bm27Zm27aQ27a229v/2/+22////7Zm/7aQ/9uQ/9u2//+2///bcfAU+QAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACXElEQVRYR+2Xa3+aMBTGE6vOaLfV0trrVunWboIXsBdYmvP9v9ZOEtEEMAxWbV/0vFD8QZI/z3lyciTkI/ahAIS9fSxTZ4346+jdMRESfTCtk+gyzRvp5DRNBRP4x6Y/cz/rWDf/7PaFIfiUuGZ+A6aIYlhK5ADrMT2cTdR43tff+RCeXI/SMd5obpqtTOG3gr4vI3qwUBhpq5zJZNwBE4T94ZOlAz+aR5oplFocLGA5oHSIhChMzOSVEVWmcRhK6RRQ2k0wzWNiygYzdjS3h66YtE7g9xII5BVnhxMSqYxlUWmaKiYiZwYf57RTCUvW+WXlo5A7znDU6sPlWwdC4ZaGAB910he5iZeD9o3x9g4m4ZUzaddXhpl2DcHZF2WHkvoUGX62ckfg4YypPaZ02sZURyH9bAaxWrmOTtJPWdp2wSTOL1Ra6vhJGX3jpwqdlOkdUcgd3E6EJxuIf9x3nB2T6T1+vFzKtKU6gU6PT3VlcwUKv8kdBDhdKuv9hqlYn/D5tbdC2hrLMjV89uiYS1fJEu6AEtcZDdxS2ikFNJnApy3USc65YSrWcfiBa9P296rXLb2froeJ07kYldILD+UubrRX7AtstNg8jMS5pVPWaoWrqlPvDG4kkXr1n8bpya+so7TQau2eCWaYNo52WrLWhLNukl4n3DZA8+O6oUiPs25CUumUFA+LYaL6GdtPe2dSB6muBJGxQV6n1WqoE6J0n3UliAcoWUnsXyciTu6Uf/78Br+T637UBqjozxuL4RqoS23MehBgo5Z/8n9area4/LPzf0rzid/3yL/KbUvESH1i0wAAAABJRU5ErkJggg==)
Let us take,
![](data:image/png;base64,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)
[We have done this substitution on the bases of identity sec2θ – 1 = tan2θ]
Therefore, ![](data:image/png;base64,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)
Now we know that, cosec2θ – 1 = cot2θ
Therefore,
![](data:image/png;base64,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)
Question 7.Write the following functions in the simplest form:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASQAAABCCAYAAAD+I6sfAAATBElEQVR4Xu3dBbjsRhUH8FfcneJwi7u7vuJWnOLwCoUWKW5FP4oV9+LQQile3K0FirtToDzc3QrFzo+3w0u32bubZLIvdzPzfee7e3eTSXJm8p/js9Om0goHCgcKBwbCgZ0Gch/lNgoHCgcKBzYVQFp/EuDPGYN+WebKKDhw6njKfwT9bRRPO8CHLIA0e1BOFj+9IOifQXsH/WuA41duKS8Hdo/u9g3y9zt5uy69LcKBAkj1XLJSvn4yKR8Yf49ZhJnlmJXgwM3jKZ4WdMugL6/EE22ghyiAdNzBAkaHBn0/6J49gdHjot/HbKB5ssq3WvcO3DYe+ElBNwn62io//NCerQDSsUfkhPHvq4NOG2Sl/GtPAwbwXhf0hp76L91258ADoov7Bl1zsjh177H0MJcDBZC2swgvnhB0+6ArBf18LvfaH8A+YfX9Zvsuypk9c8Di9KqgXYKuFfSXnq9Xug8OFEDaPg1uFB9fG3SroPf3ODtOHn3/KugUQf/u8Tql6+4cOHN08cmgtwWRmP7TvcvSw3ocKIC0jTsm3qcmQLRXzxPv8tH/i4IuXabmhuDALeIuDwki0fa5UG0IZvR9kwWQtkmJLw7aLegyQT/tmel7Rv9XDdrS8DoXjOOfHnTHoN83PLcc3p4Dx49T2fzOF0SV/0P7rsqZ8zhQAGnTpssFkz4a9Nigp85jWIbfnx19/HgCLvO6u3MccP6gnYOuE3SSoIsG/WbeieX3rBy4ZPT28aD9g9gZS+uJA2MHpOMFX98+ecmpUL/tic/Vbj8c/zwl6H0LXMuLQBr6YdAbg65cAGkBruU/xHtyUNANgi4VZEEprQcOjB2QiOCko/2CHt8Df+u6ZNC+eNDPGl7vzQWQGnIs7+Ek6Y8FPTPoEXm7Lr0lDowdkHjVbhhEEhEI2Xc7S1xAoN3pW1yoAFILpmU8hTT9wSC2vEsEWVhKy8yBVQek8wS/jgqqc9eKL/lSEM/JrTPzdVZ3140fHh4k2K5pGxognSYeYI8gHsqjg/4UdHBQXfzWGeJ79jBJq4zEJwgS4zOtIpuP1w5iM2M8FhpBkmRQdrzE19T8JmbsVEGfD/pIkPOFb6wFSYjGs5w5iBwKAmc5Jl5euZfyMRMHVhGQGH4vEMR9v2sQ21Bd9vZD43u2HDlLvCjLaPLizhV0vxYXGxIgXS3uX+gCcH1nEMAX3S7d4nlB36g8HxB+SNDdg7ZOvjc+zw3iRPhQ5dhHxWf5Y++ofHeN+ExN4plM47gWn28WdGAQIHxZEFDyO+Mzu5soeDxznVztTNHRtyb3KFgyJ9jluscN3c+qARKV6D5B1CJ2GkGO/k4DkhWaPeDcQRcOWpbXygvkhfECNW1DASRSp2BBNjfgkxqAeEvQc4LuP/mSAZjTgNTz7akHpvYAHiqz8SJFvXVyLImr2ni35P8ZRwsOYJcAm5Ke7xKfnx+0JQifLEYA815BL5zqq+u/ANjzeLYSad+Vm1PnrxogVR/vkZMJWgdIF4rfvhjEJnDjzDxdrzuruJfk0y2uORRAAqY3DRJ+8IvKc4jholZxEKiUwOYCcACIF3habaa6WRTYYoDZWYO+GkQtevcUfwQl8kr+PYhK9qOgr1SOIe2KpL5IEDWQGscITY3LHQ1/j+hT3Jo8tyogT91y+bcNB8YKSLL4DwjaJ8jKuozmBf1zkIJvbfKimgDSWlxDDae24/u5OFeYwXRjt6FSASIq1Hov+znjd6obqQfI1DXARUJiKNYn1VmAKgnsiMlfi8YfKyefPT6zK1XVJcB30iCxWn2ndwA9tkfhG9dfwvVmsG41v247YTcCN9aTkKgRJv4Vgj6zpIfx0hH3z9vyek0ACRiQxNqOL0murhLBOeJ7MVEkj3mG+avEMdTTVwTdbcYzMwzftTIOSr8IPGQAJ+Vo7EGknwNn9HHK+B5Ius4yghblIn5hcn9JIms5pOW0aQ60nbAbgZOzAClNKKv9xYKWEQyJXzx5vELKmrRpTQCpTf+LnMOjplIBwNo85wQ5e1TT9QBJsCHwEXZBBTMfSV0y7QG4a9xpMk4kMtedblQziwrjt5iyZTTJttRIgaqkudIycWAWINHTDX6fJTgyPcLMbmYBEhcyVeKzQfPUjpz3mAIvH92y0yEAEqCQhKy8L5tRXb0otiHqlFirxOdZdjq2IjY+C4MFgq3plVP8OXH8TyWjwjFsTzcGdN4+0krVOaEvHrw+VDjeQON57yCqf2mZODALkAzwa4IYD5fdGDh5YJo0k5WtodpmAZLwfy+CDO47NLlIx2N5oFyzzjazSNdDACT3mTxYddKB+fTgoGcEkXQkA5MIeaSqdiD9CBMgFeHJw4KogzxjwGsaRKifjn9ykJAJ3jbHuh5jN4C8+uSa+j5d0G2CcnvY9K0JFXlTECM+D99GaXgIRE8UNMiKpXWA5DsvLG/CjgAk5R6smE0asXm6NMQsQGKPENdilXtik4t0PPa7cb6XTRxLm0ZKAALCFKrerTZ9dTmHlETVEmLBDsdQn5rnsynCeydfCJ5kN7NYkG4S0JhjYpak7vDYCYIESEcGXS+oqno5ltrH+QDk2G/MT9cGdMaQJ2/z5JqcB8bYOb/7/53l/ZDURAthFQjzXiVfb+KnALl32j0Do0HWC68DpMvGzR4WxDW+IwAp1zDMAqRkt2DPkTqyjNa2KBvXMhWT+iPAU/yUyHOqkJfbxBIYuOxGjSJFbw5SildUtPikrUEkh2qjiqmk4KV4z+QH3ikJqiSeBGgASUgBSdAK7oVxruBWXj9Gdiu834GNEAB8Ick/K4i9isEdn3jv8KmvJkSBLe0nQexffZU67nr/nBtitkhxQFw8l9CKwbYqIKXBpxNzrZJU0n5k3KzVAXYed60HZi8wQCbidEF0E8iq6XfeECI8l7e+BcL5zsr/9R44NAuQrN5WYS7iaTWvh9v4X5e8efjK7rJKDTABIgGKWyd/Zz1fOtbv3wsCKNUGhBCAooIxapsrjiV1pUYCUpLFb2nBNB8BGsCWk9iH3ah6rzyAXmxeQVHnTSXWvtNeLGLUYKolAJeR0GZbp7PFeWvHGqX6f2BD02Tx2p6qgGRloQ5YkbhiiXjJA2VFJiprJoRUAIib0FY6hP/tY1Y18lnBeCPYaoTaM2AyNlpVPQCR23l7BCUxf4HnX+gQq7L4l2pgJIMrV/QVg9ipqsF1C3Xa8iBpE9zgW1qeX04bFgeAK6cPQzpwbPKyr8XxfaW9MHWQXAkLNAGmCVJj0wYXvOPCKKjo67W0b2GW3L46lc3L85Ig0k+dyga0iNPEYi7ZtBoxXko8JAVMpwnIZ2J8ZEeQv1QVcd8V/1sZHdN1ZbOyElGBJikIILJhWI3FHrlvwEodtYqw6yyjSacwMRh7S9v4HCCJsVsyb6C6cIS6p+wr7UWIBY1AjuFLgwBRU6mter8Wcqqofnjaed23BhFAaDUpVSf7SLYBJKIxnZ5EsyUogYi8MOK1h6HXVxvD3+FBYk6AVrVBViCGqdVs7uwPGx0CLFIRNWMW4PZxXYGE7CWzajJ3BeI+7nmV+8wRfydSmzbRJP4pd9oLqZsm4P2hnUgk/nXHgfNeUPVUNk3zUv0n/xMkSGHShnqxv7YBJM9rhWA7csM+c7OSnLx4LPlQutoSINUNHkDye13OWUfeHud0EhM7F9sWUGKUXEYTH2MQs+jZy7jhco25HGgDSLnSXphIxGt55wCF8AaeyhyNtuLdTqk57GScJw+adM78QnPqJQi1LSDRK+3uCfF/EER8pRalcIGhAxLeLqs2NYM+qYwRv7TV4UACJB7DRcoR1z1527QXUgyPpEU8NyBN36ewDAJHClgliUku7sX+uiggJZcu1BRbIshPTAhQSpXzUp7TRpCQPPd0ZG9frwpbFo/HvNyvvq5f+u2HA20kpOk76Zr2kmxH4rkEiuZQ2ar36D3hpZNdkDzhwJcKt6jdrBH3FwWkfSdILEKWeAiIoHPV6D0NSJiVEleHorKJB4Ls7F3LsiGJXCaqpxpBjQaoHDxYDuQApFxpL8m7RloToyUuK8d2XkIa2IO9v+xHyZjPgN7LHnV1gMTwzGVIT00uQ0XPiGnc5rxUwgGmI1SFDUDNJCE5J5X2GAogKVHB08bDVn2+Pmc9Xqr706YoW5/3VfpuzwEv5ieCSDgWXnmR8xrPb99pLyn+iMebF1wRO3FZbRuvMHVNWI6WAEnYTi8e4zpAYlvBYPFDH5jchPpBilFhKjc6dQcApWRG3wsXELKf3I4pRcODpPwxagvDd7VBYHFBJK42dYKaMLvqrnW9ZUStAnD8a1OUrcmzlWOXxwGGX55mkokQkkXSgcTcLSvtJUVob4lrqkclMLJpdUuVHRQx3CcoRd/DC5IhZ5Z4QmabrK0OkHxHzdg9SPzM2uShUhQ29YPkI6Yi1SsWHMYN6CbFGvmsRINIb9HZ1DmFyYiRSIKfmAkBmLsEkVy2BnlYOU59NhnggJHURnJp24Awr916u0+QKEUeO65LekHZtbbtKPVzHmO0xcy4kkoWqYqxI9JeOFQIBupRES4AUwpwnscZ3jQS1vQOK95PJhtxStMJ0/P6nPv7evEYmK6YmODBunwp4fOQWAEt7vMUs2D1gJzVcP+5N7LEA0hk8tjUJ5rOu1r0NgCNeCq84RKd1ayeUmPaFGWjOgP6nYOkueTatVY/bAwicauJsYs+ezlu204rorMtRiTtRfm4o9JeeHjlRRIElI9hA1L1cr1GSACi07Yo3wsFWASEG8+VHAFijS+6g08wGELirRxcpk2bkAcS4FoQFdBKMauRMq0mcveaNv0Ce3Y8JUty7VprVSclSuWp1g9qen9jPp6qxjnCjkTSz6669MRcQMJ8IPWFJjO4NkZASrVseCNmlVadNVDACDgAIiBDQhLsOctwCPhM1vWkqEUmRc5aSAWQFuH4+sfwZqlcYGEibZeWiQNjBKS0uh0WPGRLapK2QScXqs/QJ82F6qOMxiyPg3gtKmJb1TANcwGkTBM+UzfyJY256GX5XqVl4sAYASmVjgBE9P8uhjmAtl+QUrh1TW6fzOvpZOOmwzdUQBrj7rXGjttbRcpUJrfpeJbjZ3BgjIDkmSUGqy7Q1fXPuM24J1RiOrtazRteRn+72hiGCEhsJ2PcvZbTRsDvWhCnRclPzAivYwQk7BN5zn2pjIK6yF3agXEy46aSLdUmtkreT46ibEMDJKlE8hcVuhefltoYdq8VpiIERowO+2FKQu0yh8q5Ew6MFZBSDhHR+3YdZ4OXUHQ61azafCfHKEW5drnM0ABJ1PlYd68VLqKcLlsidb20jBwYKyCJpRBpKyanbkeMJixWY0mshpisqj1KUKlKCDmMnk0ASYyMFAUxL3XNM7N/SC04esYx7Gskn7ryLFRQ6TdU1HnbSOGJaqOrtHutrHc1v0jAvSSYNpl8q3bsWAHJOPKS8JZsDjq848AeGufzpB1S6eew+GxHDBGyXVsTQBJIyQvI1lHXFgEkHkRJ1HUJmimJWgrQvAoGq7Z7LSM+MBa/RfqdrgvedZxHf/6YAUngoZw9BeL27jgTRFWrDUXySM2klfOXI6K1CSDNe5SucUhj3r3WhhUi74u7f94sa/n7mAFJcCPpRVoHb1uXPbyE2B8VZKsf0oXdGoTmy9/L0YYESIJDx7p7rXHYNYiaTx0vLTMHxgxIWKlMA3VLkm+qiNeWxdIx2ItsWiCSV66Y9IwcbUiA5Hn2CuLyH9PutRYuNiOR+nvmGNTSx3E5MHZAYk+xLRI+sHfMMvIuMnfYbWRGm6zAiJSUqygbNSHXrrVdVTa8GOPutTLfqfaM2X3sI7jIHFv5Y8YOSAZ4tyBbJEmEtfq1bYy9VlA2lgODGMq77FUlO7uPXWtzABIejWn3Wt5CY8txITm1tJ44UABpW6Ist7QKkjwni5aSqBsSRnIGTy5/ak0q4dvT8LXqNhcgpYuPYfda4ylezR5sbTZebDVQYzypANK2UZcCcESQvdOI5m2bCHCGbaK90p9dirK1vYd55+UGpHnX2+i/i7Qn7VpolHEurUcOFEDazlwgIp2ELalpuc/Ui32ySEXym6hbQ2zsZvsH2TliiIA5JJ4JelXMngdWuZljhnRzq3gvBZC2jypDrbw2xmhesrYv65FxrlynNkXZVnGObeRnUsdKChBDtjIzpfXMgQJIx2awSFwrojgb6RdNaiWlntQt5q2T61TaxuWAIEhOCQX9eGJLWwIHCiAdl8lrE1CSOqEAW9PGME7K6lqUrel1y/H5OGBrI7FfNvispgPlu0LpqZYDBZDqJ4aNJAU4srUc1HDu4Kl8sun6SA27KYfvIA6oKKrSp9IqTcd+B93y6ly2ANLssVyLn5SZMCkPCGqjvq3OTBnHkyhLc/BEMhIKUtqSOVAAackML5crHCgcmM2BAkhldhQOFA4MhgMFkAYzFOVGCgcKBwoglTlQOFA4MBgOFEAazFCUGykcKBwogFTmQOFA4cBgOPBfWKurfxDjTggAAAAASUVORK5CYII=)
Answer:![](data:image/png;base64,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)
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![](data:image/png;base64,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)
![](data:image/png;base64,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)
Hence, ![](data:image/png;base64,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)
Question 8.Write the following functions in the simplest form:
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
Dividing by cos x,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
As we know tan(Π/4) = 1
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Hence, ![](data:image/png;base64,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)
Question 9.Write the following functions in the simplest form:
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
We will solve this problem on the bases of the identity 1 - sin2θ = cos2θ
So, for a2 - x2, we can substitute x = a sinθ or x = a cosθ
Now, Let us put x = a sinθ
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFUAAAAmCAMAAACCnScHAAAAAXNSR0IArs4c6QAAAIdQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOjoAOjpmOjqQOmY6OmaQOma2OpC2OpDbZgAAZjoAZjo6ZjpmZmYAZmY6ZrbbZrb/kDoAkDo6kGYAkGY6kNv/tmYAtmY6ttvbttv/tv//25A625Bm27Zm27aQ2/+22////7Zm/9uQ/9u2//+2///bGpwtdQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABdElEQVRIS+WW3XKCMBCFs2k1pS0V+wstaEtVSMj7P193F0TijGORvel0L3Ijfjk52T2g1F+vAmBWlQBvsgcpdK58KgxFImpdyCpFmjV3sThUqRI9EK/m6fnqS5rqs7xJ5sJUX+BN1SB7XT4FjVpBGCt89Kk4/wEQV1MpdTjUPp1XbvotH1FranJeJKuY4emtGeSHjT5/v4HLAHRc1RRrtHwbwAFHAxDRJMOOHKGcwse/ozDWZU2UqxL5LZVWast9nTAE07ar/QMsx972VEYvelY4lKXuHOkxpzxZQbSm3zqt+DfaqB3yVvGheup5gzc3cI3pE1IPvl7kAO26NSgppCrugSYZvkNG3BZZyogjKodyPYzQMZ1lzatyS9TKU8AL3RYZi7N1adS5zADck1TsVV66hHNL0A/nb+XfPuGxH2myRYty0tP3i3wFiSaGl6f67SN1oZhCBpGvYaZL8DkSxB2goXYvw/ePhFa1wm7dJdLGTpT2A9M1H5Gg+hV2AAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
Therefore,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Hence, ![](data:image/png;base64,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)
Question 10.Write the following functions in the simplest form:
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
Put ![](data:image/png;base64,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)
Now,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= 3θ
![](data:image/png;base64,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)
Question 11.Find the values of each of the following:
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
We will solve the inner bracket first.
So, we will first find the principal value of ![](data:image/png;base64,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)
We know that, ![](data:image/png;base64,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)
Therefore,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARcAAAArCAMAAABlwjyEAAAAAXNSR0IArs4c6QAAALFQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OgBmOjoAOjo6OjpmOjqQOmZmOmaQOma2OpDbZgAAZjoAZjo6ZjpmZmY6ZmaQZpC2ZpDbZrbbZrb/kDoAkDo6kGYAkGY6kGZmkLyQkLbbkNv/tmYAtmY6tmZmtrbbttvbttv/tv//25A625Bm27Zm27aQ27a229u22/+22////7Zm/7aQ/9uQ/9u2//+2///bAcULvwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAEzklEQVRoQ+1abUPaMBBucW6yF50I7k1xblLcFGWbrCX//4ft7vJ2gYSElVY2zAcKIcldntw9d9c2y57aEwJPCPw7CExPR9ur7KMpVw3yvdttxaUR5eb9PM9PIlsuj28mhEsBg58/mNFJk5uG0yiHghYU/HvZ8z7b54plJC5Z5oxPnby2euISDoBa7Mhoaa3ckoJrC2ZHvo24jEflq9us7J6nbWw3cKm+3GSZwWXWs34bQmkncCnfYOSz9jI5jDL+LuAy75PzMD+aRD19F3ApDshbGC5iGCPfHcClfCnzxxnEP827+H1le0xcOlLfpuO0MhcKvWX35DdKjRrMRClXO06LsbTWhX2GDkVcdiGVePapeVxMaC4AFzHsoEg3P1nSkSmXvKHARu/eDtbChS3TsL1wj7BSkxOZ1IMOeuVkS3EpvLFn3o8xr91ovRx8ERcxHeT5fkLJvMpeZnlifho8rnlfn5czRAyjodqMD+KiGX1ROBV50Ej3RVyK/Cyr+jHej/BLfVyAab2YIdsktiAuM0bOyX5EYWCiznv+TmpRqStfpVl+CSHLA04EnxAuY7SJvVtx/zrPe5AHgIHcdfEbb6J4oaoOvozWSgz3EZh5f2HWEt2rydVFnnd6DyjKkVeCb3bAPOGqAgvpwLrzIyiFMjUfvjWIS0b2IoYHD6LAb2X3cGQsQWEzsRU8x8VYK/mz39c99oKjxWeYQWHDyiu76Jvn0HOWTW1pzLurIYVjNR8sNmDr2pITfEkpiDdiZNNLWj9SepKyIUJn+2TREFT9OTjwFbIeXChalEcGFy1Pxxa8wjnpPZlu7EGZZn4YF2tHy/tdwCqBXywu4UBnl3GySjFk9+UM9Lk/3x3nh9/JQaS9wAfK0zLl1QRgt5t+6fkWFysRRK7wL/iLK7fk6BwzaS9iego5KtfTb4MGF3aiOJ3jEuVd4DJkpBAupLqOKC4uUqqav0l+CfgR8suCnhFcCu425EeBFMu5v6t/TLuwv1X2YqR77AX+o/kpuNT0IzKadfyIbnLMFAtp3vUQjIdfkFrIT1x52gBdQzRMI3M1nGLmK409B7iJ/AU59vorfFTv0dWJsqK8S8mgKCQuKr30BiQfLhh3sOAiUVbeBHJFcT2CHrjefdKI2G5QEcGhACULtmBet4F8F2gMkgZIY3q/+vl5iSyDqW4gILlhTQ6qPkhDKdU1wi/VBcg4xv2BKC4P8qb9K5gM185HG5N09z2Mx5u3ej6dSKAO8HZ7maFefcTcPeEoWPVUI99Vdyj9PKd6ddiitNTUa2FzpwjjlHZt4sKqpxq4jM9WQkJ/6uSr6FyBky2nZD7ucUu7VnGx1VMNXOKoyMQHm1Ov2eTHt4Q71L2hmCLSPyYdXplzNoxLxm/+6yiU4IA2IU7f0ErQ0peRWjaNi8WgujzGohJa/EFJZgN5+oY2g4uqnprGRYOAIRRiHLYEc2GlXcu46OqpcVwktWCbdslCo08D3CHt4mISi+ZxERf6ifQMky74GWNPJ+tpFxdTPTWPS5b9UDctKW2pvsVgAQtjBUuruNjqqQ1ctGMk3i92SrtW4zSrntrCBVI6Kp7izSntEh8UxldNehVMFfcn7b1HVuETzoQ3XzAF5C9Wbew9sjhyTyP+HwT+AOJC0/YJIAYQAAAAAElFTkSuQmCC)
= tan-11
= π/4
Hence,
The value of ![](data:image/png;base64,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)
Question 12.Find the values of each of the following:
cot (tan–1a + cot–1a)
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
= 0
Hence, the value of cot(tan-1a + cot-1 a) = 0
Question 13.Find the values of each of the following:
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
We will solve this problem by expressing sin2θ and cos2θ in terms of tanθ
Now let us put, x = tanθ. Then we will have,
θ = tan-1x
![](data:image/png;base64,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)
Now again, Let’s put, y = tan∅. Then we will have,
∅ = tan-1y
![](data:image/png;base64,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)
Now,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Hence, the value of
![](data:image/png;base64,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)
Question 14.Find the values of each of the following:
If
, then find the value of x
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
On comparing the co-efficient on both sides we get,
![](data:image/png;base64,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)
Question 15.Find the values of each of the following:
, then find the value of x.
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
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)
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![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHcAAAAXCAMAAAAGEyDiAAAAAXNSR0IArs4c6QAAAH5QTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OjoAOjqQOmY6OmaQOma2OpDbZgAAZgA6ZjoAZjpmZmYAZmZmZrbbZrb/kDoAkDo6kGY6kLbbkNv/tmYAttv/tv//25A625Bm27Zm27aQ29u22////7Zm/9uQ/9u2//+2///balKiKgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABZElEQVRIS+2V227DIAyGoVvLDl3SHVkbNpYuJPD+L7ifhG4hENjFVGlSLPWmtf3Zv41LyGL/UYHPe0rvzl+43h1IvarODwaxvfoDrkwUb44Q9TKAyGK+XVNfx0KCgJYluII+k668ePej6tR4xepAOh7J+fEyzqLLpxR3A19JvQgik1slYiGW2LJxGlGo3JIocAWl60ZSW4ECVvmVBCKKqUTWYzxQddNkuX0SgeoMB06XFJbkdvvtGziD59i+O9S7iuS4gz6Go99gnSCDsx/RLG7bxBbPcCeD4cgErhzKj2UBcKC17PbX1+LIYjojlftanaqdl81wuyfT8eSuhqIoNqGzjU/rLDZOMv3wGDYRVagXJ/LCJ4ciyZVrYBWSmNdKl6fWE+0OY7FPYGr+O/LXO/C1B9GIov8gW+JOuVBjT0aHJQy4/t1AMjr/gJ2OheFwsvPKg7s9w/9VdJ9zW7H8viiQV+ALKcIYLYrTF1oAAAAASUVORK5CYII=)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 16.Find the values of each of the expression
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
(For
type of problem we have to always check whether the angle is in the principal range or not. This angle must be in the principal range![](data:image/png;base64,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)
So here, ![](data:image/png;base64,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)
Now,
can be written as,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Hence,
.
Question 17.Find the values of each of the expression
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
(For
type of problem we have to always check whether the angle is in the principal range or not. This angle must be in the principal range
.)
So here, ![](data:image/png;base64,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)
Now,
can be written as,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAC4AAAAmCAMAAACMNFloAAAAAXNSR0IArs4c6QAAAE5QTFRFAAAAAAAAAAA6AABmOgAAOgBmOjqQOpDbZgAAZgA6ZmZmZpDbZrb/kDoAkGY6kNv/tmYAtmY6tv//25A62////7Zm/7aQ/9uQ//+2///b98og1gAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAl0lEQVQ4T+3U3Q6DIAwFYPBnuE0FZQx5/xcVjZjo1TmauJiM649S2qZC/PqEVi5HIal02pe98EWN4Mncmbuc+qqdufpqrDYm8tBkb0z/FVIBk4ZZZmAXdlH3AdZ4UiLvb8zpZOgXL79gqTL7guFD9WK4UY7g7vEh+PDUAuehias0costSZdmDONzj/FkjnCuqzF/ovBpREfJRgZHSCXihgAAAABJRU5ErkJggg==)
Hence, ![](data:image/png;base64,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)
Question 18.Find the values of each of the expression
![](data:image/png;base64,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)
Answer:Let
and
, so all ratio of y are positive and
and ![](data:image/png;base64,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)
Also,
as ![](data:image/png;base64,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)
So, ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Hence, ![](data:image/png;base64,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)
Question 19.Find the values of each of the expression
is equal to
A. ![](data:image/png;base64,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)
B. ![](data:image/png;base64,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)
C. ![](data:image/png;base64,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)
D. ![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
(For cos-1(cos x) type of problem we have to always check whether the angle is in the principal range or not. This angle must be in the principal range
.)
So here,
![](data:image/png;base64,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)
Now,
can be written as,
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKcAAAAmCAMAAACWJHujAAAAAXNSR0IArs4c6QAAAJ9QTFRFAAAAAAAAAAA6AABmADpmADqQAGaQAGa2OgAAOgA6OgBmOjoAOjo6OjpmOjqQOmZmOmaQOma2OpC2OpDbZgAAZjoAZpDbZrbbZrb/kDoAkDo6kGYAkGY6kGZmkLaQkLbbkNv/tmYAtmY6tmZmtrbbttvbttv/tv//25A625Bm27Zm27aQ27a229v/2////7Zm/7aQ/9uQ/9u2//+2///bSPvszgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACxElEQVRYR+2Y2XbTMBCGR12oWVooSSkOS+NAqVsgxo7e/9nQSCPFbix5ZBudwkEXcY6j5dM/mkUB+N/+WQXkR0Ft8aT3uFnXL+6gzt7/EcrdUoij9eDUzadvg33AcVaXW9O7UArPo+5ueTYMAPWr4a3AnhPK8zuadbdMyLlbsozZsnt5Soom5Sw4mrf1BJmTjCk56+ccqwNUx3s/wu/YUnIy5YRScy5+4a6soNM45cZakuFH7FBTKE6ZH73TQiL0VD3vX19FcNKKjLDQ7kK7m6YnlBGchfXdKFICTMfJOBl9G5C53t4ITkw92DAWRuipPMMrpMz9gRVP6yjO9moRnJXeWH8LcZY6Hfv1rK9UxlZT4/MCs3KzUi9sxjXryeKZyxfmpPpHWc6+emgCZ51dQ6PynH7mOlKcbuWHji+UaH5jTTp9gVFGF4C+eijIqe1AemJBYpoteqx36uCMwUH3rC9Iv8f2I87AKMvZyYs0TYjT2MFnd/vePPXnRpzfek+Y4QyN8nE+lsgpJoReLYZT5kjx8FKc2DqrX88uZ3fU3o8O62D2+Tywe48yCu175qt4vHq6UbNwHtjTaIF1AHoOnk99NL05xXCGRu3Te7seMgtPiJ+luAb5Za2Ox0L5u4LVruzyucePAqP2cb5dDzE4B/LRfSZObvBUZkJg1GxW6ssbj7vbuAT+UVZrZZR2PTSkJw0bkTd7fZ6RvSPqELnJbKAmMyTkrBj3UaNBlV3+tGrQqISc7KUq5QmukRXYg70R3vzAsDu4y2N4rs5U9oqakpN5Le4UVnZvKTmZghbHn1WJZgozt7WknMC5ccpcvN2qzId1hbu+j6nnx8YlXHfVrV/7pqKLBvqP6m57zKcn638w+OErZBwycWLSar7S2/n+BxsIBzE/mwtRRFaImXzGvnV2toWHwG1qxrUmTYV3LF1a/K3tN1iiYAsapnOBAAAAAElFTkSuQmCC)
where
[since, cos(π + x) = -cosx]
as cos-1(-x) = π – cos-1
![](data:image/png;base64,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)
Hence,
.
Question 20.Find the values of each of the expression
is equal to
A. ![](data:image/png;base64,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)
B. ![](data:image/png;base64,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)
C. ![](data:image/png;base64,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)
D. 1
Answer:
as ![](data:image/png;base64,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)
as ![](data:image/png;base64,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)
We all know that the principal value branch of sin-1 is![](data:image/png;base64,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)
![](data:image/png;base64,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)
Therefore,![](data:image/png;base64,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)
Hence, the value of ![](data:image/png;base64,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)
Question 21.Find the values of each of the expression
is equal to
A. π
B. ![](data:image/png;base64,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)
C. 0
D. ![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
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Prove the following:
Answer:
Let
We have,
R.H.S =
sin 3x = 3sin x - 4 sin3x
Therefore,
= sin-1(sin (3θ))
= 3 θ
= 3sin-1x
= L.H.S
Hence Proved
Question 2.
Prove the following:
Answer:
Let x = cos θ
Then, Cos-1 = θ
Now, R.H.S. = cos-1(4x3 - 3x)
= cos-1(4cos3θ - 3cos θ)
= cos-1(cos3θ)
= 3θ
= 3cos-1x
= L.H.S.
Hence Proved
Question 3.
Prove the following:
Answer:
L.H.S.
= R.H.S.
Hence Proved.
Question 4.
Prove the following:
Answer:
L.H.S. =
= R.H.S.
Hence Proved.
Question 5.
Write the following functions in the simplest form:
Answer:
Now, Put x = tanθ ⇒ θ =tan-1x
Therefore,
Therefore,
Question 6.
Write the following functions in the simplest form:
Answer:
Let us take,
[We have done this substitution on the bases of identity sec2θ – 1 = tan2θ]
Therefore,
Therefore,
Question 7.
Write the following functions in the simplest form:
Answer:
Hence,
Question 8.
Write the following functions in the simplest form:
Answer:
Dividing by cos x,
As we know tan(Π/4) = 1
Hence,
Question 9.
Write the following functions in the simplest form:
Answer:
We will solve this problem on the bases of the identity 1 - sin2θ = cos2θ
So, for a2 - x2, we can substitute x = a sinθ or x = a cosθ
Now, Let us put x = a sinθ
Therefore,
Hence,
Question 10.
Write the following functions in the simplest form:
Answer:
Put
Now,
= 3θ
Question 11.
Find the values of each of the following:
Answer:
We will solve the inner bracket first.
So, we will first find the principal value of
We know that,
Therefore,
= tan-11
= π/4
Hence,
The value of
Question 12.
Find the values of each of the following:
cot (tan–1a + cot–1a)
Answer:
= 0
Hence, the value of cot(tan-1a + cot-1 a) = 0
Question 13.
Find the values of each of the following:
Answer:
We will solve this problem by expressing sin2θ and cos2θ in terms of tanθ
Now let us put, x = tanθ. Then we will have,
θ = tan-1x
Now again, Let’s put, y = tan∅. Then we will have,
∅ = tan-1y
Now,
Hence, the value of
Question 14.
Find the values of each of the following:
If , then find the value of x
Answer:
On comparing the co-efficient on both sides we get,
Question 15.
Find the values of each of the following:, then find the value of x.
Answer:
Question 16.
Find the values of each of the expression
Answer:
(For type of problem we have to always check whether the angle is in the principal range or not. This angle must be in the principal range
So here,
Now, can be written as,
Hence, .
Question 17.
Find the values of each of the expression
Answer:
(For type of problem we have to always check whether the angle is in the principal range or not. This angle must be in the principal range
.)
So here,
Now, can be written as,
Hence,
Question 18.
Find the values of each of the expression
Answer:
Let and
, so all ratio of y are positive and
and
Also,
as
So,
Hence,
Question 19.
Find the values of each of the expression is equal to
A.
B.
C.
D.
Answer:
(For cos-1(cos x) type of problem we have to always check whether the angle is in the principal range or not. This angle must be in the principal range.)
So here,
Now, can be written as,
where
[since, cos(π + x) = -cosx]
as cos-1(-x) = π – cos-1
Hence, .
Question 20.
Find the values of each of the expressionis equal to
A.
B.
C.
D. 1
Answer:
as
as
We all know that the principal value branch of sin-1 is
Therefore,
Hence, the value of
Question 21.
Find the values of each of the expressionis equal to
A. π
B.
C. 0
D.
Answer:
Miscellaneous Exercise
Question 1.Find the value of the following:
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHMAAAAiCAMAAABbTxaGAAAAAXNSR0IArs4c6QAAAKVQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OjoAOjo6OjpmOjqQOmZmOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZpDbZrbbZrb/kDoAkDo6kGYAkGY6kGZmkLbbkNv/tmYAtmY6tmZmtrbbttvbttv/tv//25A625Bm27Zm27aQ27a229u229vb2////7Zm/9uQ/9u2/9vb//+2///bBiODfwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACQ0lEQVRYR+1Xa1eCQBBdLCtSS9M0xUrRMtRKIPb//7Rmdtnl4SKz+Klzmg/iQe7cmTsPVsb+rVKB+HXTRJ1wcGgCE5iou2yGDXofzYAsGc3qkHx1g49sO07rKf9scNUwU1/4O2Xb+zE+w+cLtmvlNeHesA5r/D26JSgbqLjw6WTsCAN5wotG6tanCaEqzvhlyth648/SOzaJpgXCBnJrq5lx+s4lcDKmOVlATjQtEMJpIK3tXoSYcdJClkXVTnxK63H/Gho0eVxKWbiH2v5gzyYjehcpzmRU27UQIHYM+N66clZwukK3j5zcOx1zMtL9pvOMXHqcxrb3yQXVnCF2/DkWiIGNYHxa4Amvd7hI4zncKO5GWSCwjJMCMwQnOCN3ymIQXFw9yBwl588F2VWBoFRqr1BgJj0CFEo1oph1bDPRWtGdzKtsmtMOlrlBoVTzyqv4XDm996qSKc5TMNl5RyZdHnNyD7PddZx2xV5U9Sxy1sKyFDBoQ8DwwN6tGEMzp3JSCStyyhDVsGI9RSmr1o3aXZawjFPMZ+BMGV8vQegh9C20q+hI8QI0mN4JdrAcpxgI2FDtBVbRdRycyngOX8SiMpjKzxKmPWX4qi413Cft+Gp/jXZnWDhs1AW7m5QEs4On7m1eRnz1UC5RM5kszm76pavlIJwZTdLRYdzrT7pFbS0CLnCTcZE7+P5Kx196oMdbzpZ08kMGOJuwfIQ2p74SKZ/T/nhwb3DIzyPg6vr8xO+ftJNxDKeAXHjx2xmUfxD6CwpbRLOJ3jEIAAAAAElFTkSuQmCC)
(Forcos-1(cosx) type of problem we have to always check whether the angle is in the principal range or not. This angle must be in the principal range
.)
So here, ![](data:image/png;base64,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)
Now,
can be written as,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
where ![](data:image/png;base64,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)
![](data:image/png;base64,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)
Hence, ![](data:image/png;base64,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)
Question 2.Find the value of the following:
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
(For tan-1(tanx) type of problem we have to always check whether the angle is in the principal range or not. This angle must be in the principal range
.)
So here, ![](data:image/png;base64,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)
Now,
can be written as,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
where,
[since, tan(π+x) = tanx]
![](data:image/png;base64,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)
Hence, ![](data:image/png;base64,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)
Question 3.Prove that
![](data:image/png;base64,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)
Answer:Taking LHS
Let
![](data:image/png;base64,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)
Then,
![](data:image/png;base64,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)
Therefore,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
……. (1)
and
![](data:image/png;base64,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)
As, LHS = RHS
Hence Proved !
Question 4.Prove that
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAN0AAAAqCAMAAAAAja6JAAAAAXNSR0IArs4c6QAAAJlQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OjoAOjpmOmY6OmZmOmaQOma2OpC2OpC8OpDbZgAAZjoAZjo6ZjpmZmYAZmY6ZpDbZrbbZrb/kDoAkDo6kGY6kLyQkLbbkNv/tmYAtmY6tmZmttv/tv//25A625Bm27Zm27aQ2/+22////7Zm/9uQ/9u2//+2///bHTVPNAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACmklEQVRoQ+2a2XaCMBCGE7vSTdtSuyhdxLZYq2De/+E6E7aoICE6zkXNBQfPIb/fPxmTGY5CHMYhAv8hAj+XUnZeGJ1SAkSdgRA/8p7NHiWACs7RV3g6Y7JHCpCLa48cgxZgLjEzOyMOZ/o7aQGmHuwqfOaEoASIPdhQIjlkWztKABXgfpJeWQYpwMJP98yjbxZvQpACZKvGeSLotCECiOTtjPc0JwXAQujkY495qcbLh+veASi9Tm4e2EoHSl+5dnRwl4civuCsNFYWuw5m4Us9sGpotXZz4jpq0qaOsYFp426MITn6Vrj19LAolcOJh3ehlKezKA3XNiP2SoUmzVoYA0CFZ5sLIxUY66XDBY3ETIV4F3tXo7RwxI8q2NYcZJLxZU2atTCFPYi33Nwsr7vTk3WUswvUxliHREXTDWHPRlMm57+RYoLRQyxpVkiWmbkC45o9VYILH13F3jVkaN0o4cu76mdVUJahmzVFPcy6tBVAKqimfWjU8rVL3S3llGvwUNtw16C5AcYSIMK0Tfy8aSlS3cjM1N3i8akM+m4yc0mzLjNxE1iDsTQHW8a6O22xTHXtTr2Osv7CVrn6OXNXadLUHFUwrgjY3H6+wyV5xl1lnqbnvVAhOJxv/y7PPBEaNetgXM0JMZadIVxk79eXwxh/fbjr3QWw1eGN9avKSXXNY5zmqlmzGsaOoQbAOTLTvnaEIeF5d0QIkDxAkVMclM4hcp9ICRB3vyJWd9QAvO7wRKYML6m4TcaSAhTiV5484WgTSQEycfU6EInZd9iEfSfPkAJk4hpUv/Le9yAFMMV3UrW1jQ4pQCaONRvr2tEAZAUydtyJ2ea0XQLn5+kA1BsWYMfwj4CkDzfdL2dGx4nsAI7cztP+AIhjVMsUjfjwAAAAAElFTkSuQmCC)
………………………. (1)
Let![](data:image/png;base64,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)
Then, ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
………………………. (2)
Now,
L.H.S.![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJQAAAAgCAMAAADDuaGFAAAAAXNSR0IArs4c6QAAAIRQTFRFAAAAAAAAAAA6ADo6ADpmADqQAGaQAGa2OgAAOgA6OjoAOjpmOjqQOmZmOmaQOma2OpDbZgAAZgA6ZjoAZpDbZrbbZrb/kDoAkDo6kDqQkGYAkGY6kLbbkNv/tmYAtmY6ttvbtv//25A625Bm27Zm27aQ2////7Zm/9uQ/9u2//+2///be+boogAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAB10lEQVRYR+2XW1vCMAyGUxSdoI6JMDwwdIyd+v//n027IeGwdW0ueB7tReFie/v1a5pkAP/jjztQzYV4zllM2E7E6JWDJOMZVNGMBbX6hGy0ZkDV0RIguWcgaUT5wCFKxmFeoTCWUX0s3DhyQ3zBmAp9YuqAl4gbN1Hbp/mhqHq+ABl7HB/l7QJH09NDCWXgKQqg5dUvayi7RRXikmYiCrLALiVY8LZBX0qgkDoSeqBQKuo0MGV8bjvuPKvQdxN1Gd3HU29WKyFGYV6gKzgpT0MClMld92WjTvnzQN2kcS7fx7kJuTKYriEl0ZXiKXZmcCLKhZeYUFGjye81lozycS9KKxtWRYgoBp46p42YfumEb5xSk+aeG/sNmT/4yMkmB/Aa3Nmlsom4/bYSdSF2j27fcN7pztRKu0ClRwun7ER580w4QfIb6F3HZyOKgYcGLaDC6qaTnZ68Ap2Bh2nKlI1S/Sz1hMl80PUjMcXAs8ro1/6Q6YVkjLfZo31ptol52b8dbnoh+ZaDXPn3saljL3V8dPtiWtAC6XTE3KI4jFJFVnXWTtuhL7VOFf4RpcE9naed4kYUi1G4In5G+o62t2IxCnfG4FTbW/EYJTcqI7h9Yvma2/v+DxVzL9T1jIavAAAAAElFTkSuQmCC)
Putting the value from equation (1) and (2))
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
=R.H.S.
Hence Proved.
Question 5.Prove that
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
Let![](data:image/png;base64,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)
Then,![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
……………………….(1)
Let ![](data:image/png;base64,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)
Then, ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
……………(2)
Let![](data:image/png;base64,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)
Then, ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
…………… (3)
Now,
L.H.S. ![](data:image/png;base64,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)
Putting the value from the equation (1) And (2))
![](data:image/png;base64,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)
![](data:image/png;base64,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)
……….by equation (3)
=R.H.S.
Hence Proved.
Question 6.Prove that
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
We can also solve this problem by using the identity Sin(A + B) = sinA cosB + cosA sinB
Let
and ![](data:image/png;base64,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)
So,
sin A = 3/5 and cos B = 12/13
Therefore,
cos A = 4/5 and sin B = 5/13
As R.H.S. is sin-1 we will use sin (A+B)
![](data:image/png;base64,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)
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)
![](data:image/png;base64,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)
= R.H.S.
Hence Proved.
Question 7.Prove that
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPAAAAA1CAMAAABIrpanAAAAAXNSR0ICQMB9xQAAAi5QTFRFgYGB/wAAAAD/AAAAqgAAAACqAAAAVQAAAAAAiIhmZoiIiHdmZneIZnd3d2ZVZmZVVWZ3VWZmZmZVVWZmf39dXX9/d3ddXXd3f3dVd3dVVXd/VXd3ampqf25ZWW5/e2pVd2pVVWp3UWZzgHNISHOAf25ISG5/e2pEampVRGp7e2pEampVVWpqRGp7bm5IWWpZcVtISFtxbltIgF0zM12AgFszRldqM1uAf1kzM1l/fVkxMVl9bls1NVtubFk1bFkzM1lsW0hISEhbNV1dbEg1NUhsbkYzM0ZuW0g1NUhbNUhbbkgdakgdWUgzHUhqbEYdWUYzHUZsbEYdakYdHUZsaEYdHUZoSDNIW0gdRkYzHUhZRjNGMzNZMzNbHEdXNDRIWjMdHTNaWzMdHTNbWjMdWjIdHTJYSDQeRjQeHjRGHjRIRzMeRTMeHjNFMx5FWjMAADNaWzMAADNbWjMAWTMCADNaWjIAWDIAADJaADJYSB0dADNGNB4eHh40NB0dHR0zSR0ARx0AAB1JAB1HSB0BSB0AAB1ISBwAABxISBwARhwAABxIABxGMx0AAB0zMx0BAB0yMgAdHQAyMh0AAB0yMgAdAB4eHh4AHR0AAB0dHQAdMgAAAAAyMwAAAAAzMwAAAAAzMwAAMgAAAAAzAAAyHgAAAAAeHQAAAQAdAAAdHQABHQAAAQAdAAAdHQABHQAAAAAdAAAAAQAAAAABAAAAAQAAAAABAAAAAQAAAAAA84FQcAAAALh0Uk5TAAEBAQICAgMDDAwNDQ0ODg4ODw8ZGRoaGxsbGyQlJSYnJygwMDExMjIyMzMzMzw+SUlKS0tMTExNTU5OV1dZWlpiYmNjY2RkcHBxcnJycnNzc3R0dHV1fH5+fn5+f4GKi4uMjI2OjpiYmJmam5ubn5+goKGhoaKioqKnrrW1tri6urq6u7u7vLy9vb29yMjJysrKy8vL1tfZ2dna2tvb3Nzd3d3d6enq6urr6+vr7Ozs/P39/f7+/v2CTqQAAAVRSURBVHja7Vn7W1RFGP5glnXOybjYYpmBECwUlkVcA0xLrQyEIKB7IRVZaRAFQjcDQ9FcsrI0uxjEQkEEA7vp/Hc9c2579uxZPLvz9dTztO8PcPiBd973nG9mvpkXIIMMMsjgfwBCaY747afUj0y9hVJKCSqltEqy7chlNgRAdoUYu1iKKm77HOd8pRzz40irzNq3NFOtAkDlqyoUheZvxzTcwRgTLxMP0ipJz0a79qA8K1wHVxsQ1d3xbgFuOSOobPqrPe4FLtUilt8oP1Xv/wcWHQmV2+fOFMQWAeL/ALP+ysIswi/tRF9jZVR28afeZJGLpVrl+XZ/81E+qra7ngxH5+/E9SulUjm7cliFB5fX7hV/TLAIH9iKPOk+uzGGS5iOSmJujYHZabEItBqilJZF3i21oSeuUYFrvxbKNwp23tRVkqqrFfpTcHVE922KKluWkBfjtaN1rULWr5M3VZU1zNQQmB3TK9sieE/CcIzXjuDXsl84kTdVlYGvDAJlStvClXNnVHMVs57SgMVrR+OkKlvSCbypqowR1ESbCUCV2Ne2+AlA7uftHtbJZN2xQ5hPdOi+fvnO0sbrXWUSgsHf6mnJl0MARdcu3Ufz+o96+PfXk81Kh+H+E3fTvP69gGjYTSXJTvphNOTECzsYZguHRFkfY4x9Uu1l/L6Fcndih+GWMGNvFUvsuIm8biorn0jy/4OMGb2861xLHxbxv8KbdbIzvcUFMEtv8wNaNiKvr4f3iqoV5ZCt79nEr5/vY0W/49v7SToV5teni7ZouRB75e3odBzoc8x7COPJGunmvMqHEb7BhiD3OGN/vEIg9+krDz8UWh+41dHUs9SPG7nvsJkHXgYgJcevVrgSe+W1GyYln7LICdEb5x4Js98H8m0jeeOt451aJ1EMz/EGGFznb1dDK0/9/JhFLegve7QTlMERgLKfomsVEsTxhquW9kLZ8rQKt5yfVKFl/cLW2EjeoBueOK2SJvHUISQFV1PvkNuYhXa9KWsmEHhJ68vEtpQ2cZxh5dywWPZ/LISuFTFPW3m3bSTvhsVN1SOLNsMj0guSMrVWbzQc79sMj6RRNz291tWedXehnJ3W7zKmVdtI3g379i0effymhqk73IlbWPT7/TneDCdl1epmfUP8rNXVNsSd27RjTGykzXjjDJM3Vsr1p011MXe4z2EoOsaujxNPhpOyOku6zjzoBWa/ULUP/UuhbaTNeOMMB1eHwYPhVOYwEICikPZBJEraaTi4rF2IEKJMaZcQgdlh+0jeSrobiPbiGnk3gS60OfxiPkDln6IQR4XhLhTDyhQfv43Sxlpoi/YaxxjbSJ5uzpbH8x7dszi/c9fHN8buKT3Je7OzmviFfPlF67UC+szPhUB2zPHmbJ8EsX1bqolc53xlUgVlIrqfbpsaso3kEX1sphgOhhcOBX5YODAhKlJU52nZQ6ny2J6QYNbaAPaCDHGb/XBXFjJOGEofYwuHVdtIGWSQzgUZofY2ndIcdF7sUFIqkSS7n79iLSFmjojh1+JFDyXlEsma7y5z07CVIyIgxoseSsomknWmYStHxIHBix5KSieSlmFHjohk2Lh2Qgsl5RNJU1h8johqGDOUlE8kTWFxOSKqYeRQUjaRNOeaPUdENYwfSsolkoYwR46IWtKyoWTiLaZMImkIS8gRURctqVDSBTKJpPWFnTkipmGpUNIFMomkOYcTckRUw11YtDpkEknzksWWIyIZ1nnTi/uSQjaRJLSJj+ttvpUjovQHJm8KoaQnyCaS2mneuLQyc0Sk/kDnTSGU9ATZRDKDDP7L+BtZaTYDB/hjDwAAAABJRU5ErkJggg==)
Answer:![](data:image/png;base64,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)
Let
Then, ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Let
Then,![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Now,
R.H.S. =![](data:image/png;base64,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)
Putting the value from equation (1) and (2))
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
=L.H.S.
Hence Proved.
Question 8.Prove that
![](data:image/png;base64,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)
Answer:L.H.S.![](data:image/png;base64,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)
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![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= R.H.S.
Hence Proved.
Question 9.Prove that
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
Let
Then, ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANQAAAAtCAMAAADhnbX7AAAAAXNSR0IArs4c6QAAAJ9QTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OjoAOjpmOjqQOmY6OmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZjpmZmYAZmY6ZpDbZrbbZrb/kDoAkDo6kGYAkGY6kLyQkLbbkNv/tmYAtmY6tmZmttvbttv/tv//25A625Bm27Zm27aQ29u22/+22////7Zm/9uQ/9u2//+2///bhgBQ7wAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAADNUlEQVRoQ+1Y61rbMAy1ywrZYDCyslvDGE0ZZO3WXPz+z7Yjpbfc7DrBabav+ZFAPsvVkY5k5Qhxuk4RsIrA74mUN1YWw1+cfXwUi9Fs+I7aepi8dQhqeddt87b20a1tGA5en07k2cvBq6sL9faabCzclVRy/Rx1AWWwjxvrJnKHiSKvAxVKeb6KpJxqcqmxn0tcZy9q8Y57XYyNfnnc9WL6V7drB/KYQIkQoVaB9td1QeFMqeBipWgjkXiXMxEhRJlPcI8FSgXIlL6ijaA46IkHCOubuw6xze+eU2Db+trWQuK9N7BfZ7+rqR2ozO8XVB2RI9MZac6UWt55TDZGNgBQ2afPhu5oBEU1tUe/44NS97PMv9C2IiMo5mDf9NPwS4Xgfyy1RaDjZ+LdiqcfuKVfiHlxzkHXNaUewHb55mt9LlQgR8iUbEaltxdiLkdT3OTNH19OE6os7XYdT6eT+UAjoB5AgdVAnbNySy3xfTmmDwvqqqmhi1ltfbzFofwmUp+OGe6qzSPz8Vy0/+WQDhiaH0V4DurxUfGvXAlIhsYp6Hn1DK/Te7zYVBCdDWAfXq+PchWYBp8BAE88ItkUicAzANloslbfKTd0hfyGQOV3PNqCqpl3XwV/zb5MLfKeXCaKcUaSq/zteobMh+/KvLOdyg1/NPl+qH3TuqZ9N/Nh/uT7XF7+XC9XQf52L1OvElzHmxRB5RTD5/OY1ZQt47Y1FdHIk/obclo51x/9ajIFT5ceUy3E0M9PApGh8NAM24OyikCnxetkcHvIS4jLiWFEdIuBgifpuIts1MlHe+MIR6x6mvEXQkrIuA1OkClW3fjrAUWFicL1yG/hu1FLh+o0fqRKwmRPp1N6jz+uKVt50yEs0BxHH+p/tK3Cutmtjb1jLb2isBoEsXJg9PY6vdydll5VWO1AGex146ZDLb2i0BZAtVBo9+2bFVoUi1PduSScFDNlr9AW7JsUWoTSKaayll4EZa/QVkHtxrWdQtujlt6bQtu3ll5uFLYKbU2mjq/QlkBZK7T1NdW7mFmcnko1Za3QVkENQKEtONVCoS3YD0Wh3XeqjUJbzPRJobUYiP/7pX8BzSxrasK0QxYAAAAASUVORK5CYII=)
So now putting the value, we get,
R.H.S. ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= L.H.S.
Question 10.Prove that
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
Consider, ![](data:image/png;base64,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)
On Rationalizing, we get,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
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)
Now,
L.H.S.![](data:image/png;base64,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)
= R.H.S.
Hence Proved
Question 11.Prove that
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAU0AAABFCAYAAADO1LQdAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAA2ISURBVHja7Z2/bxtHFseHFOAqVspczhp2OTtdzBG7w1UJtfKPAC4IiVwIAeSACAhhcbYUsDAiSp0A/6iTSxHbjWX1SRHZ1TWJ3SdwdP4DbOlPkMXbN7NDrldLcX/N7K9n4AEWuaJ2385++N6bN98h29vbBA0NDQ0tmKET0NDQ0BCaaGhoaAjNcBdGSAUMbzIajhE0hOYU2yOkapnGFcMwV7s7Ox8k8HDNZNkyBKHc+Glnp/uBaRirhmldIWSvijBAKy00+93WrMnovYZpLSUIg2GWLUPQzJ2fLLOxRJl5r9XtzyIQ0EoHTQBmh9H7bGXrqgIYHGfVMgbN3Plpa4Vdpaxz3z59TNXRygNNqE0BMKnRu60CBjhYiu2nnkFv0+baBtY40UoDzUGbXad0cTeJGqYHBDMIzeL7CWqci5TusvbgOt5PtMJDs9/vnl+g9KmxvvWZopQToVkCP22tG59RuvC02++fx3uKVmhoQpRJmPlQIQwyUzfMODRz7yeTkYcYbaIVGpqQVhlz5FnSkz9uGLj+X3FsBicNiuknmBQic8azpMs8ObuXOM6LDM2BZVympP5iZTD4WMHgGdXpYBD1ei3WbLJNSskr2lxbxwFUPD8NBisf1wl9YViDy2UFJo7zokNTU2rOI5Ba7Y9ajfwJr+NgKq6fypyi4zgvATQ7jDxi5tY11SnnaFCZ7FqUwTTk6U66qY6qc0jST5kAB5w76zwqMxjyfP8QmmcYr2fCrLmiVCpJGKw16XrQ32mdWgIoQOd5PTT8wpxDHqCpyk+85EONp7rqmva/6tlLQFval8oiNAsKTVF/qu+rrmfqhCZcEyPkwA4JT0TaWzmBhn35uv2z/Rp9G6W9SgU0k/ZTmHuvyk8qx5XX+r3WxTolL89eAspe6zgXhCZCM3b05NdCoyPShAi6w8hPHAhzzeeyb5DXbwk7aFuDT6JckyJoJuqnsJmGCj/pgib0Fxu0su8s83wH4JdLPsWXQeWd+Ln+F0IToZkMNBWmUZMatXVAUwJhkZJfoQh5uf3dl91uaxZWrMRp4FcFzTQfOhV+Ul32GfkI1rwb7U0Yv3wss8790d+fI8/SBBZCM6fQHPeK+del4kBzmqxaHBgMx+c9sm+a9Fva/OZbn5pVZVoKakcar+fn6W6YXtSkzkGVn4jP+U0xJX5KE5qn/OV0gYx6jxVNcJYFmtP4UThowoXe6X3OKKGvJg3eKNB0PYTHTmo5kzQ0QfzBq7BTEenXO+/r0x5w5+856edO4OV9cc9BtZ9gyWKNkDfBFIpqb6ZFjlH9lCVoSl85XwKvEZpq+VE4aPJ+Mf7A0KOEoTmSCZsEBAmLNNNzeeOFEAn9L9S44qrwhDmHtPwU9QFJ0k9pQNO+NxtuaKbdYJ93aAbhRyHT82mDJ4mapp/QxFnCEzqhaX9T1ildfGJtWX+Duh0MgM97d5gOaKblpyiWtJ90QxMmhJpz5LmMLOW4t6+hLkstCM3k+VFmaO7FhOapKCogDDZUAqvfb12Yp/NP5KwpV+Ah5BDqdq1+/0IK0NTip/DASd5PDjT3dEATIuLv2pe/dEdEMj2H+nO32/qwzdggxdnzjSwzAqEZFppfXbpx7tynB/aA+ijmwH0PCH4wkEVlMcDtY+vLj8MIGoQBFijQQ+QhJm3E50O0ARM5/G/PNZ+3ev2LYVPQuLPnOvwUCpiK/GSPu48+PXfu4NJXgxvKxzjXTiBHhLD/STAKaJN9x9cnqpYJT4K4rvuH0Ix4c86aLdWRnnvTz0l1ukkTF0GV4rkyeMBjoffQ+/mnJ3amT47EOYe0/BTGVPlJZ3ouxjj5y+sfqMlxP1L2W9R+00gRpsb7p5Id2qFJNKyTPnv2VAx0zdA8RsFh9JNuaKKpYYd2aEJhnTWtrzOfnifc3C6BgAOz3H5CaBbDtEETakLLdfI47VkziHahyG9f9EuYCfWrS6lYEYQq7egnhGYhxudUfiQCzT1CqrKIPl45sld1v++nKuNTa5DKz1XvZ0QNwf0asHWr0aCVwxCakUHl4sPkZ/50TfL0sS7WVKOUC4PwI6pKlnegPBHCATzgFCtHWOcneB9mKr9gtR/Hq0vo4dzC0rb8UHi/3WTroPYMAq6WaVxhlPwGq1BoffmBis2qEJpoCM2MRHW91sV5Sn+R4iM19sWPrW5/1nss54TBbo+BRt8CH9zHwjELrPYf/j5MhPXa/2LMHCSdukdVyTpNaJ+mVrkWFiSq5EyeadBNOE425DpqMxy4tXnjB8O8tQivW2I2c6hiSRhCEy0NaA5DrZsv/h47Yrli5bBhWksyyuO9sp69lnacJn5CF3+Vr1tmY4lzw7X8teMqD0olKxWi0FFVsgJDcwFWWtAFfrHjhtz3j4M+QC8gZR+aiiZZhCZaGtD0W9c/ybLUqqPMVwBCTy9ph9G7Xkk7WCpqR2+HXr/KwAoYIRv7QbHK3TrEWHtT1fmHVckKBE13GA4rFNbajbYNwrdhoKnimwKhiVb29DxJtajIz6D9fE/LJEfZqs9OnyNG2O/BUljR2E+Pmku9ayrOeVKqHlQlKzA0oTC71mYdgCVlnbtWk32dN2iGHFxoBbUsQDOpc09CLSrOOUheTIOmjCB9oSnfcxTqIWUfCTFT+oq11zpRJpPDWBiVrEDQBNJ36vQBD60dp/sdlwNoHqOhZaGmqercIwI88jkEXaPuguZz7/PqmjMZLSUdWO1PmvO1752/eeIs56wouv5QKlmBoDkG37hukUdo6o4KshI5aUwVC+EnrGmGTs8dgZTBBZ/SQWXsU5F2S/WmU0B1+OIGFsATunBUTSZvb4dXyToLmhvyAvy+TcQMk3hNXqQo9BYSmsMsW4agWQg/YctR2PqvIy5iR4OtbvdD+SUFjHDXB+HLRkRyvAe84oIWn32HY+Hzmqy56W5B4lAjlaO4ivx+FkUli/jVSPgv2Q6AmSTTMFYty/inmPgRH3Sn1/rHfK32c4U7qvO412vVQU0GVhKNG+OH0Og0mmXnijM+fVs5gmZu003N0My9nxCaIeuBQvD3HRn1PILRQ3drkfTrgpipPhF1SjIDE8scuk4/uIQwZeY9G8CzcEyPB2PsIGl5vKgqWb4fJtoFnMZSp1dpzWjcFAXn2puGsXZTqrPwn1dWbvKWJE9aciqNcVqW8ghNfDjK4yeEZgRw2sGWk0bzZ7023/zer89R9EY6fHEmpxqG+W/5DHPfGyYP1Eafp0jpKapKVv7rKYqhSSbs641WXD8hNNHOHOsIzWApJw6W8vgJoYmG0MSUE1PznEFTtDW1ZlK6l25hnipJYY8ihGZBoOlSbyrFmuKy+iltaILvRCeKaPbW+XdBeKNOycvRhA6tv3RW5uB4R2gGGkSjOh0Mml6vxZpNtglKTnnepQ/9lG1oihYcvm+QVmjK1h/3RIhUAYJ12TjWEZqBoidZp+NtFbXaH7Ua+TPvW5uin7ILzX5/5e+MVn4XsNIHTXHNlX1qtDfl8wSN5bJFSDfAEZo5hqb3taj7QQ817LuUhdQ8rp/KDE2+XJnR+9QwN6UUoy5QQcsQtBL6+oKfy3iLYYQmQlMLDMJsnxtVUbps0FTlp7Sgydc/M/OeW782C9Fdh5FH7nXhCE2E5iQQ+G9RqxiacRSlUwJmon4KfO8V+ikNaEJaLpfzZQmao3NxVuygITRDRU+6Is2oitJZiTJ1RZqq/KQbmkMnLZeAzxI0xbpv9jtGmQjNUZSURWjKByesorTKaDKL0FTlJ53QdNqL1t1qSFmBpoS5CqEMhGaOoOmRCxtOAkIcGPjpLYIIwHiHz2A1t7CK0t6HMY6it2o/Jak4HsdPaUOTR3L15QfuawURC76XDgjkWNZcGk3ufjBHKwI0uWhIfT/Mt7FHiWeiZFgcaPrpLYpN55wdPl027QEPoyj93u/FVPRW7ackFMeT8FNS4yqqTdLmFLXainMP3t9rRwcwocThN5uOVk5oHrv/7xdFTZrc0JmeuwdvUEXphB+cVPwU5yFPyk86oTkx0k0pPQe/QfTrt5EZLKlEaOYcmkmkUX5R1FnrqHVCM6yitOKHSYufIqe4CfpJfF56G/alBU25y6y3XAC23r1xiTHjLm5imHNogpmMPGTtwfU4EZU3igoIg1BbEoeFZhRFadWRpw4/hTUVfuLrvj1b0hYdmryGKTZOPJqkfE8NC+ubRYAmfzhjbqXhBYIfDOTExUiJXmz0FFiQIgw0oypK6wanCj+FAqYiP0Ezt6r9aIJCU4h666tlyh0g49SVEZo5MTGDvvBU9ujFTT8nNmtPmLgIOrsIBf+gx0ZVlNaZpqvyU0i4Je4naDKvE/oClwyiFRaack+ROCm6J4pC/cwS+4k3xlNjH2t3aIWFJo9uVtjVqp2ix01XJRBwYJTTT0Iwo/oIm7nRCg9NsSqE7nr3U44KBBwY5fSTMwu/i1EmWuGhKaNN3iYSs7EZrZy20++eh/Y1jDLRSgNNMNgaFGaoUZofLWxazrsbWOcu+gOtVNCUeyrDpBCCEy0wMNuNNgAT03K00kHTDc6GaS0jONGmAdMyG8sITLRSQ1PaLdNYNAxzFR8GtElfrqZhrBrmrUX0BxpCEw0NDQ2hiYaGhobQRENDQ8uV/R/6hkp5LLLqrAAAAABJRU5ErkJggg==)
Answer:![](data:image/png;base64,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)
Let
so that![](data:image/png;base64,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)
Now,
L.H.S. ![](data:image/png;base64,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)
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![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= R.H.S.
Hence Proved.
Question 12.Prove that
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
Now, L.H.S. ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Now, Let
![](data:image/png;base64,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)
![](data:image/png;base64,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)
L.H.S.![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAF8AAAAjCAMAAADFciZ9AAAAAXNSR0IArs4c6QAAAKJQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OjoAOjpmOjqQOmZmOmaQOma2OpDbZgAAZgA6ZjoAZjpmZma2ZpDbZrbbZrb/kDoAkDo6kGYAkGY6kGaQkJCQkLbbkNv/tmYAtmY6tmZmtpBmttvbtv//25A625Bm27Zm27aQ27a229uQ29u22/+22////7Zm/9uQ/9u2//+2///b9fZafQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAB6ElEQVRIS+2W2VbCMBBAE1S0gopQpbRuFJEWXLok//9rzqRraLqlh+OL89DjYHJnMksmhPzLX0TAo4mcyvb77lRkwWWPDfjIpKNlb/PfJqWzbFe4JJJeprG5RSJj1dMAW7yR/Wid7vLXsl6GhWcQO/e+Jx+XR9cpn78Eki6xcFVsX2nwPXCKbyG0URJ+1BUCtXVrdvSfbwpH9hj+z+04IKGIrtDVwhZZJJuP4d+aOd9LcNxeEVGdqa4CxF3dB0rGDwEv/PbGPxieXK8Y4Pa5dfRjSOvqKeOzObYrrmKLV0hBoXdJpMxP9ia03P8C4+Vl2gXdskbBj26CruDYoXQ0C0L0FT++UfRokk33sjOsapTb44A/QcGJfo6M6Zp4UibENdlcym56k4KjlZpkc9iLx035wkjHzqgNUfnm3tDpBy4s+MKkQnIv5T/aErGf0AtolnZ+LagpPrjpYEAHDeA3nUBUmlvkF+JfF5+2QCj/HxkWifGGEf0lPsPzW7IUOwald1g+UPvig607tIC0jtprU//xWOD9Sev05s6k7/jN+dwpz2H1qTwLZsQAyeewmhHOcAbpS/x8PD4kFnvYcdtKXgA64tLKeJIwydMRmkpbDm2vpwHxwZdBa/l9GfjG0hMYQRqvSz1bhPwC1nEpK99/T18AAAAASUVORK5CYII=)
= R.H.S.
Hence Proved
Question 13.Solve the following equations:
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Hence, ![](data:image/png;base64,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)
Question 14.Solve the following equations:
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
As we know,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
We know,
![](data:image/png;base64,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)
So,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Hence,
Question 15.Solve the following equations:
is equal to
A. ![](data:image/png;base64,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)
B. ![](data:image/png;base64,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)
C. ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEgAAAA8CAYAAADFXvyQAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAMRSURBVHja7ZrPTttAEMbXzRV6LiXjW9UryebYI7Ic0XKz1IB8tZCFciAgHxA4uUXqC/RWqRdQH6Etp75Dq4J4ANo+giHd8Z/WcWLHSWzHJIP0iXgDTvLLzLc7s8t6vR4jxYsgECACRIBWHpD4kXxVGBtIBCgCxzQ1rij8HID9BOWwQ4BC6up8h8nyd1lmPwSsAQGKA7XPXxMgAkSACBABIkAEiAARIAKUBOiYAI0WqpWzVm0XAbH6249lKloXHzkddUtm7E5AccIC1TwiQI9ABIEAESACRIAI0JIA8hZopCRADok5lGJFe9AyplbWgAa+lia1cgFEKZYMyCFACYDIpJMNuvSA/p8eQX16UiSg0vsPwrFb/I1vxvde1zJdx3Il/MduqzXge+/wMXYwgbHfaXvfK+E/bV1/ZfT7a8H1oQIdVlW/hsdWGlBU7g4KqF9yB/RYDDoqjKC0mwKZ+k+ZzxoGsiz9eUNW36eJnkwAheGU+awhSnyb0j7n57ptbxQyzYcBlf6soYCDqcX17k442gsDNGSAMwAauG84n7TEe+POLSgHJ8FiEa8DWLkAijPoWQG5xpnyf7SRVoUHNjL+D7apwtFo9V6/TpNqEyFMu0DMG5Bt6xucsRsRbg/ee5AecEYKxsW1GINfaqe7lWstNmkKj3uuiAjq9421Pc4+uJCqypVhWesuPLec4Dettv0i12LVh+P4UVIpG6AAUhPYZzSuWuts1zC0p02Ay6wiZxIgJ/gdB2IeQIOhytrTgQInYRMd5yVx6Sb85LbRgMs0ppt5u2NcFAURNiugcaYpYZXNpPvo+KQP7b+en2r99UUAGkm1JG8qKsXCbQwA+IZ+hBV6mrVN5g2zaM+nLIBOze06QPOi3W0/Qz8Ss9efbfOULwLQUBSlBHScJyDL0jYb0LgI1jJBnwf9SLOszUIBhaMozn/mPWs4DSBLzFhKlV15pu7dH40fjd59beFHmmm9zCLdpgHkJLVX5z1riMad9m9xDRS9/6jxy3dZTPnTlhfOMu9gZFKLLev+Vy7VPAEisb8zrdteUeep3AAAAABJRU5ErkJggg==)
D. ![](data:image/png;base64,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)
Answer:Let
then ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 16.Solve the following equations:
, then x is equal to
A. ![](data:image/png;base64,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)
B. ![](data:image/png;base64,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)
C. 0
D. ![](data:image/png;base64,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)
Answer:![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANIAAAAmCAMAAACGRDV/AAAAAXNSR0IArs4c6QAAAJxQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OgBmOjoAOjo6OjpmOjqQOmY6OmZmOmaQOma2OpC2OpDbZgAAZjoAZjo6ZjpmZmYAZpDbZrbbZrb/kDoAkDo6kGYAkGY6kNv/tmYAtmY6tpBmttvbttv/tv//25A625Bm27Zm27aQ2////7Zm/7aQ/9uQ/9u2//+2///b6sRmPgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACo0lEQVRoQ+1Y23LiMAy12JY2e2m3dIG9hi2ml3QhNfj//21tJXacBtuCgbTjwQ8ZZiKfoyPJsgJjp3WKQF8RkHdQr3FflMfmWczFpycmsj/HJuoT/ySpz2jvy3XK0r6R63Nf+SG59lCgpPHLnBBHubgkWB3NhErPlSSZD34RHHm+mVpJ8v76ibBFmxSjR6Jl2MylPwggghRGksy/rciw4suBrj1LT6Y2hiX4XDCYMjfDxvI7oWLFR7+RXE4Bzt33cfqdFbE25mZSjUxappGke4pe6ynUv8IsxdCbUw6/2XriosTpd5fk31FLknlVgGL0qLtLfAXSxDVU4a2LFvbuhbeeAQxuV6XOiH48Z3DbgpT8AqPtzIR+SRxguCqq7DaFul0+JoZK7wJHoinz4Ur+VSWCHovsav4qeso/AH2IyoGt/UCWuLKSeXUsMRf+VbVdKr0LHNa0mSh3xbWVhLq2fnPQJGkfi3o/9x8mk3U6fQvYfBxBE2ZH5gKuHmxdYaqQpruc1DQ/VT3Uy4CL7KspXCOpa9SUJZleRdoCd52zbgCol/8+w7k67XXh+SXRsqROvY1cKEum2ZDpXeB4a1pmqugPJWnz46fph6GzxC9th6fRMxc4WHj6GDEdzqgkUsdjcjbfTKq24ClgfId3VjnGU0yjd4AjSRKZuvT0FIctFR+e9mBLJVQCkqtzWGKHZIF7CV9pWzK9CxyRtJ5lACOdJHWZ4EMPDttbXlVQ8k5ZwdnWkVfmqgcZgOD0gKUzVtcSjb4FHD9KVIvY1fkKJzTjUSnpdt2pkbT3bSZxkmusOzXS9r3B9xLNsXpSIU6NVMz3YOf/QnkP3u3lg54a01qJ/X/cTI0JpckZBVJR5UyNiUgyU2MicsxAiYNgMqv+zExJUpOb/yVVUoDo0sG2AAAAAElFTkSuQmCC)
Now we will put Now, we will put x= siny in the given equation, and we get,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
⟹ 1 – siny = cos2y as![](data:image/png;base64,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)
⟹ 1 - cos2y = sin y
⟹ 2sin2y = sin y
⟹ siny(2siny - 1) = 0
⟹ siny = 0 or 1/2
∴ x = 0 or 1/2
Now, if we put
then we will see that,
L.H.S. =![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
R.H.S
Hence,
is not the solution of the given equation.
Thus, x = 0
Question 17.Solve the following equations:
is equal to
A. ![](data:image/png;base64,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)
B. ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAA1CAYAAABBecueAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAIZSURBVFjD7Za/T9tAFMefwwrpDOJlA9bGL/wHyL0K1O3UGsurVZ2iSOWHbgjUzma1hbkb6dqhWxdCd0T+g4j8AS38CQF658QQBUIcO5U6+KQn+SzdR+/u++7eFxqNBswyIAfmwP8ZqEZBxdz44HOJgVLwNROhrRbejQ/qur6/OBEopbfA0GipRT0VNwDG7eC7ZwCob+OmPzc7iYCBS5vI7I9eGM77NVZG2j7S/8PQm2fLcIZWdTe1KIFDW0BOcxhITrCVCRhn5PvuIgF0MwGrFu4NA03AC1bzy6mAWhxrGX7FGcXADVE39VzJbCQGqmEc2uU3AHgdZxRvGa33+57HX9hEfiKVo8VaXYBrVWuX8aJIFITWoA5vY7GSAaPtQQeZ2BktqRLAb0A6t2v+Sv7a5MB/AXz+hX46JgF700YuSg6c7CAKWayIURd8lRDO7+sOzQsu5FoqYF1smJUK+6Qbfr8t2Ct9uNl1pVyaChj1D2IHMWy01zzXm6c6cJ01gnFFbrCZCajPUwtiU+Eb0PZJJpW/K5AQnCJ7R9YP7sliaqA+y1cIpw/WDu7QfHfsyXAh05Y1uOasv1WC/ImgVnVvJqIEu+ylgl6Nc6+prp5D0JwpUFs8QNYardGJQD64uzBk26THi9p/j3qeBO5LXTOAS3V321wI0g+DsnBFh/CL8tyfpy4brapVKX0dbkalUuUncz68zl/sR/EXXAfeKf9YmiEAAAAASUVORK5CYII=)
C. ![](data:image/png;base64,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)
D. ![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Find the value of the following:
Answer:
(Forcos-1(cosx) type of problem we have to always check whether the angle is in the principal range or not. This angle must be in the principal range.)
So here,
Now, can be written as,
where
Hence,
Question 2.
Find the value of the following:
Answer:
(For tan-1(tanx) type of problem we have to always check whether the angle is in the principal range or not. This angle must be in the principal range.)
So here,
Now, can be written as,
where,
[since, tan(π+x) = tanx]
Hence,
Question 3.
Prove that
Answer:
Taking LHS
Let
Then,
Therefore,
……. (1)
and
As, LHS = RHS
Hence Proved !
Question 4.
Prove that
Answer:
………………………. (1)
Let
Then,
………………………. (2)
Now,
L.H.S.
Putting the value from equation (1) and (2))
=R.H.S.
Hence Proved.
Question 5.
Prove that
Answer:
Let
Then,
……………………….(1)
Let
Then,
……………(2)
Let
Then,
…………… (3)
Now,
L.H.S.
Putting the value from the equation (1) And (2))
……….by equation (3)
=R.H.S.
Hence Proved.
Question 6.
Prove that
Answer:
We can also solve this problem by using the identity Sin(A + B) = sinA cosB + cosA sinB
Letand
sin A = 3/5 and cos B = 12/13
Therefore,
cos A = 4/5 and sin B = 5/13
As R.H.S. is sin-1 we will use sin (A+B)
= R.H.S.
Hence Proved.
Question 7.
Prove that
Answer:
Let Then,
LetThen,
Now,
R.H.S. =
Putting the value from equation (1) and (2))
=L.H.S.
Hence Proved.
Question 8.
Prove that
Answer:
L.H.S.
= R.H.S.
Hence Proved.
Question 9.
Prove that
Answer:
Let Then,
So now putting the value, we get,
R.H.S.
= L.H.S.
Question 10.
Prove that
Answer:
Consider,
On Rationalizing, we get,
Now,
L.H.S.
= R.H.S.
Hence Proved
Question 11.
Prove that
Answer:
Letso that
Now,
L.H.S.
= R.H.S.
Hence Proved.
Question 12.
Prove that
Answer:
Now, L.H.S.
Now, Let
L.H.S.
= R.H.S.
Hence Proved
Question 13.
Solve the following equations:
Answer:
Hence,
Question 14.
Solve the following equations:
Answer:
As we know,
We know,
So,
Hence,
Question 15.
Solve the following equations: is equal to
A.
B.
C.
D.
Answer:
Let then
Question 16.
Solve the following equations:, then x is equal to
A.
B.
C. 0
D.
Answer:
Now we will put Now, we will put x= siny in the given equation, and we get,
⟹ 1 – siny = cos2y as
⟹ 1 - cos2y = sin y
⟹ 2sin2y = sin y
⟹ siny(2siny - 1) = 0
⟹ siny = 0 or 1/2
∴ x = 0 or 1/2
Now, if we put then we will see that,
L.H.S. =
R.H.S
Hence, is not the solution of the given equation.
Thus, x = 0
Question 17.
Solve the following equations: is equal to
A.
B.
C.
D.
Answer: