prove that 2sinxcosx-cosx/1 -sinx+sin^2x-cos^2x=cotx

Answer 1

LHS = (2sinxcosx-cosx)/(1-sinx-cos^2x+sin^2x)
= (2sinxcosx-cosx)/(sin^2x+cos^2x-sinx-cos^2x+sin^2x)
= (2sinxcosx-cosx)/(2sin^2x+cos^2x)
= cosx(2sinx-1)/sinx(2sinx-1)
= cosx/sinx
= cotx
=RHS