Question

Prove the following trigonometric identities.

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

Answer 1

We have to prove `(1 - cos theta)/sin theta = sin theta/(1 + cos theta)`

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

Multiplying both numerator and denominator by `(1 + cos theta)`, we have

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

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

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

`= sin theta/(1 + cos theta)`