Question

2cos square theta-1÷sin theta*cos theta =cot theta -tan theta. Plzz prove it

Answer 1

LHS:
cot theta - tan theta
cos theta/sin theta-sin theta/cos theta
cos²theta-sin²theta/sin theta * cos theta
cos²theta-1(1-sin²theta) /sin theta * cos theta
cos²theta-1+cos²theta/sin theta*cos theta
2cos²theta-1/sin theta*cos theta
Hence Proved

Answer 2

(2cos²θ - 1)/(sinθcosθ) = cotθ - tanθ

LHS

=(2cos²θ - cos²θ - sin²θ)/(sinθcosθ)

∵ 1 = cos²θ + sin²θ

(cos²θ - sin²θ)/ sinθcosθ

Dividing throughout by cos²θ

= (1 - tan²θ)/tanθ

= cot θ - tanθ

= RHS

Hence Proved