Verify the identity:

Question

tanx(cos2x) = sin2x - tanx

Left Side = (sinx/cosx)(2cos^2 x -1)
=sinx(2cos^2 x - 1)/cosx

Right Side = 2sinx cosx - sinx/cosx
=(2sinxcos^2 x - sinx)/cosx
=sinx(2cos^2 x -1)/cosx
= L.S.

Q.E.D.