Heights and Distances
A. Trigonometric Ratios
In right angled \(\Delta ABC\), where \(\angle ABC = \theta\)
- \( \sin\theta = \frac{P}{H} = \frac{AC}{BC} \)
- \( \cos\theta = \frac{B}{H} = \frac{AB}{BC} \)
- \( \tan\theta = \frac{P}{B} = \frac{AC}{AB} \)
- \( \cot\theta = \frac{1}{\tan\theta} = \frac{AB}{AC} \)
- \( \sec\theta = \frac{1}{\cos\theta} = \frac{BC}{AB} \)
- \( \text{cosec}\,\theta = \frac{1}{\sin\theta} = \frac{BC}{AC} \)
B. Trigonometric Identities
- (i) \( \sin^2\theta + \cos^2\theta = 1 \)
- (ii) \( \sec^2\theta - \tan^2\theta = 1 \)
- (iii) \( \text{cosec}^2\theta - \cot^2\theta = 1 \)