Question

Prove the following identities:

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

Answer 1

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

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

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

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

     =`cos theta/ sin theta`

     = cot 𝜃
     = RHS
Hence, L.H.S. = R.H.S.