sinx(sinx+cosx)-1/2
=sin²x+sinxcosx-1/2
=(1-cos2x)/2+1/2sin2x-1/2
=1/2-1/2*cos2x+1/2sin2x-1/2
=1/2sin2x-1/2*cos2x
=√2/2(√2/2sin2x-√2/2cos2x)
=√2/2(sin2xcosπ/4-cos2xsinπ/4)
=√2/2sin(2x-π/4)
-1