Verify

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

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;