Cot θ − tan θ = cos 2θ/(sin θ cos θ)?

Question

How do I prove this identity?

Answer 1

Given Identity

cot θ - tan  =

cos2θ       sinθ cosθ

 

Start from Left Hand Side(LHS)

cot θ - tan θ

cosθ sinθ

-

sinθ cosθ

Rewrite the expression with common denominator.

cos²θ - sin²θ   cosθsinθ

Substitute formula : cos²θ - sin²θ = cos 2θ

cos2θ       sinθ cosθ

Given Identity Cot θ − tan θ = cos 2θ/(sin θ cos θ) is proved