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)
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)