Trigonometric Equations which are true for all the values of theta (θ) are known as Trigonometric Identity. Commonly used trigonometric Identities are based on Pythagoras theorem: \(P^2+B^2 = H^2\)
We can rewrite Pythagoras theorem as \({P^2\over H^2}+{B^2\over H^2} = 1\) ; From trigonometric ratios we get, \(sin^2\theta+cos^2\theta =1\)
We can also rewrite Pythagoras theorem as \({H^2\over B^2}-{P^2\over B^2} = 1\) ; From trigonometric ratios we get, \(sec^2\theta-tan^2\theta = 1\)
We can also rewrite Pythagoras theorem as \({H^2\over P^2}-{B^2\over P^2} = 1\) ; From trigonometric ratios we get, \(cosec^2\theta - cot^2\theta= 1\)
1) \(sin^2\theta+cos^2\theta =1\)
2) \(sec^2\theta-tan^2\theta = 1\)
3) \(cosec^2\theta - cot^2\theta= 1\)
We should learn the above three equations for easy and fast calculation of trigonometric equations.