Prove the following trigonometric identities: cosθ/cosecθ+1 + cosθ/cosecθ-1 = 2 tanθ

Question

Prove the following trigonometric identities:

\(\frac{cosθ}{cosecθ+1}+\frac{cosθ}{cosecθ-1}\) = 2 tanθ

Answer 1

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

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

= \(\frac{2cotθ}{cot^2θ}\) 

= 2 tanθ

Hence Proved.