Question

tan-cot=2sin^2-1/sin×cos

Answer 1

Hope it may help u....

Answer 2

LHS = tan-cot = sin/cos - cos/sin = (sin^2 - cos^2)/sin*cos = {sin^2-(1-sin ^2)}/sin*cos = (sin ^2+sin ^2-1)/sin*cos = 2sin^2-1/sin*cos = RHS
Proved