y=sinxcosx-cos^2x
=1/2sin2x -1/2(1+cos2x)
=1/2(sin2x-cos2x-1)
=1/2[√2*sin(2x-派/4)-1]
=√2/2*sin(2x-派/4)-1/2
最大值为√2/2-1/2=(√2-1)/2