Prove the following identities

Taking LHS

Multiplying and divide by the conjugate of 1 + cos θ , we get

[∵ (a – b) (a – b) =(a – b)² and (a + b) (a – b) = (a² – b²)]

[∵ cos² θ + sin² θ = 1]

= (cosec θ – cot θ)²

= { – (cot θ – cosec θ)}²

= (cot θ – cosec θ)²

=RHS

Hence Proved