Question

Prove the following trigonometric identities.

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

Answer 1

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

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

So,

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

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

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

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

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