f(x)=sin²x+√3sinxsin(x+π/2)
=(1-co2x)/2 + √3sinxcosx
=(1-co2x)/2 + √3/2*sin2x
=1/2+ √3/2*sin2x- cos2x/2
=1/2+ sin(2x- π/6)
当2x- π/6= π/2,即x=π/3时,f（x）有最大值 3/2
当x=0,时,f（x）有最小值 1/2+ sin(-π/6)=0