[2sin2x/(1+cos2x)]*[cos^2x/cos2x]
=[2*2cosx*sinx/(1+2cos^2x-1)]*[cos^2x/cos2x]
=[2sinx/cosx]*[cos^2x/cos2x]
=2sinx*cosx/cos2x
=sin2x/cos2x
=tan2x