Prove the following trigonometric identities: 1+cot^2θ/1+cosecθ = cosecθ

Question

Prove the following trigonometric identities:

\(1+\frac{cot^2θ}{1+cosecθ}\) = cosecθ

Answer 1

\(1+\frac{cot^2θ}{1+cosecθ}\) = \(1+\frac{cosecθ^2θ-1}{1+cosecθ}\) 

= \(1+ \frac{(cosecθ-1)(cosecθ+1)}{1+cosecθ}\) 

= 1+cosecθ-1

= cosecθ

Hence Proved.