prove the following

Question

2 cosec 2θ cos2θ = cotθ - tanθ

Answer 1

2 csc 2θ cos 2θ
= 2cot 2θ
= 2/tan 2θ
= 2(1-tan^2 θ)/(2tanθ)
= 1/tanθ - tan^2θ/tanθ
= cotθ - tanθ