Question

Prove that `sqrt((1 + cos theta)/(1 - cos theta)) + sqrt((1 - cos theta)/(1 + cos theta)) = 2 cosec theta`

Answer 1

`sqrt((1 + cos theta)/(1 - cos theta)) + sqrt((1 - cos theta)/(1 + cos theta))`

`= sqrt((1 + cos theta)/(1 - cos theta) xx (1 + cos theta)/(1 + cos theta)) + sqrt((1 -cos theta)/(1 + cos theta) xx (1 - cos theta)/(1 - cos theta))`

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

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

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

`= 2/sin theta = 2cosec theta`