3. 3 sin α – 4 cos α = 0, then find the values of tan α , sec α and cosec α, where α is an acute angle.

Solution.

3 sin α – 4 cos α = 0

∴  3 sin α = 4 cos α

∴  sinα / cos α = 4/3

∴ tanα = 4/3

We know that,

tanα = y/x = 4/3

∴ y = 4 and x = 3

r = √(x²+y² )

∴ r =√((3)²+(4)² )

∴ r =√(9+16)

∴ r =√25

∴ r = 5

sec α = r/x = 5/3

cosec α = r/y = 5/4