cos^2x/(tanx/2-cotx/2)=cos^2x/(sinx/2/cosx/2-cosx/2/sinx/2)=cos^2x/(sin^2 x/2-cos^2 x/2 / sinx/2cosx/2)=cos^2xsinx/2cosx/2/(-cosx)=-cosx*1/2sinx=-1/4sin2x