解y=sinxcosx-cos^2x
=1/2×2sinxcosx-（1+cos2x）/2
=1/2sin2x-1/2cos2x-1/2
=1/√2(√2/2sin2x-√2/2cos2x)-1/2
=√2/2sin（x-π/4)-1/2
≤√2/2-1/2
=(√2-1)/2
故y=sinxcosx-cos^2x的最大值为(√2-1)/2.