Question

Prove the following trigonometric identities.

`tan theta - cot theta = (2 sin^2 theta - 1)/(sin theta cos theta)`

Answer 1

 We have to prove  `tan theta - cot theta = (2 sin^2 theta - `1)/(sin theta cos theta)`

We know that. `sin^2 theta + cos^2 theta - 1`

So,

`tan theta - cot theta = sin theta/cos theta -  cos theta/sin theta`

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

`= (sin^2 theta -  (1 - sin^2 theta))/(sin theta cos theta)`

`= (sin^2 theta - (1 - sin^2 theta))/(sin theta cos theta)`

`= (2 sin^2 theta - 1)/(sin theta cos theta)`