cos(x+π/6)=cosxcosπ/6-sinxsinπ/6
所以y=sinx(√3/2*cosx-1/2*sinx)-1/2*cos2x
=√3/2*sinxcosx-1/2sin²x-1/2*cos2x
=(√3/4)sin2x-1/2*(1-cos2x)/2-1/2*cos2x
=(√3/4)sin2x-1/4*cos2x+1/4
=√(3/16+1/16)sin(2x-z)+1/4
=(1/2)*sin(2x-z)+1/4
其中tanz=(1/4)/(√3/4)=√3/3
z=π/6
y=(1/2)*sin(2x-π/6)+1/4
所以2x-π/6=2kπ+π/2
即x=kπ+π/3时,y最大=1/2+1/4=3/4