Question

Verify
(2cos2x)/(sin2x) =cotx - tanx

Answer 1

cos2x = (cosx)^2 - (sinx)^2;
sin2x = 2sinxcosx;
Then, (2cos2x)/(sin2x) =2[ (cosx)^2 - (sinx)^2 ] / (2sinxcosx) = [ (cosx)^2 - (sinx)^2 ] / (sinxcosx) = (cosx)^2 / (sinxcosx) - (sinx)^2 / (sinxcosx) = cosx/sinx - sinx/cosx = cotx - tanx;