2cosx(sinx-cosx)+1
=2sinxcosx-2(cosx)^2+1
=sin2x-[2(cosx)^2-1]
=sin2x-cos2x
=√2*(√2/2*sin2x-√2/2*cos2x)
=√2*[sin2xcos(π/4)-cos2xsin(π/4)]
=√2*sin(2x-π/4)