Question

Prove the following trigonometric identities:

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

Answer 1

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

Multiplying both numerator and the denominator by `(1 - sin theta)`, we have

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

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

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

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