Question

Prove the following trigonometric identities:

sin² A cot² A + cos² A tan² A = 1

Answer 1

We have to prove `sin^2 A cot^2 A + cos^2 A tan^2 A = 1`

We know that `sin^2 A + cos^2 A = 1`

So,

`sin^2 A cot^2 A  + cos^2 A tan^2 A = sin^2 A (cos^2 A)/(sin^2 A) + cos^2  A(sin^2 A)/(cos^2 A)`

`= cos^2 A + sin^2 A`

= 1