函数y=sinxcosx-3sin^2(x)的最大值

y=sinxcosx-3sin²x
=(1/2)*2sinxcosx-3[(1-cos2x)/2]
=(1/2)*sin2x-3/2+(1/2)*cos2x
=(1/2)*(sin2x+cosx2)-3/2
=(1/2)*√2sin(2x+π/4)-3/2
=(√2/2)*sin(2x+π/4)-3/2
因此,y的最大值为(√2/2-3/2)