Question

Prove the following trigonometric identities.

`(cos^2 theta)/sin theta - cosec theta +  sin theta  = 0`

Answer 1

We have to prove `cos^2 theta/sin theta - cosec theta + sin theta = 0`

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

So,

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

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

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

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

`= - sin theta = sin theta`

= 0