Question

Prove the following trigonometric identities.

tan²θ cos²θ = 1 − cos²θ

Answer 1

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

So

`tan^2 theta cos^2 theta = (tan theta xx cos theta)^2`

`= (sin theta/cos theta xx cos theta)^2`

`= sin^2 theta`

`= 1 - cos^2 theta`