Question

Prove that tan theta-cot theta=2 sin^2theta/sin theta cos theta

Answer 1

let theta =A
LHS
tan A- cotA
(sinA/cosA)-(cosA/sinA)

(sin^2 A-cos^2 A)/cos A sinA
(sin^2 A- (1-sin^2 A))/cos A sinA
(2sin^2 A-1)/CosAsinA