Question

prove that cot theta-tan theta=2cos^2theta-1/sin theta× cost heta​

Answer 1

Step-by-step explanation:

Consider L.H.S

= cot θ - tan θ

Using tan θ = sin θ/cos  θ and cot θ = cos θ/sin θ,

= cosθ/sinθ - sinθ/cosθ

= (cos²θ - sin²θ)/sinθcosθ

Substituting sin²θ = 1 - cos² θ, we get

= [cos²θ - (1 - cos² θ)]/sinθcosθ

= (2cos²θ - 1)/sinθcosθ

= R.H.S