各位学霸帮帮忙 高中数学函数y=sin（π/2+x）cos（π/6+x）的最大值为多少?

y=sin（π/2+x）cos（π/6+x）
=cosx (cosπ/6cosx-sinπ/6sinx)
=√3/2 (cosx)^2 - 1/2 sinxcosx
=√3/2 (1+cos2x)/2 - 1/4 sin2x
=√3/4+√3/4cos2x -1/4 sin2x
=√3/4+1/2 (√3/2cos2x -1/2 sin2x)
=√3/4+1/2 (cos2x cosπ/6-sin2xsinπ/6)
=√3/4+1/2 cos(2x +π/6)
当cos(2x +π/6)=1时, 该函数有最大值 √3/4+1/2

y=sin（π/2+x）cos（π/6+x）=cosxcos（π/6+x）=cosx(cosπ/6cosx-sinπ/6sinx)=(根号3/2)(cosx)^2-(1/2)cosxsinx=(根号3/4)cos2x-1/4sin2x+(根号3/4)=(1/2)(cosπ/6cos2x-sinπ/6sin2x)+根号3/4=1/2cos(π/6+2x)+根号3/4
最大值1/2+根号3/4