Prove the following identities :

Prove the following identities :

(1+ tan² θ) cos θ. sin θ = tan θ

Prove the following identities :

sin²θ – cos² ϕ = sin²ϕ – cos²θ

Prove the following identities :

(1 – cosθ)(1+ cosθ)(1+ cot² θ) = 1

Prove the following identities :