f(x)=cos2xcos(π/3)-sin2xsin(π/3)+(sinx)^2
=(1/2)cos2x-(√3/2)sin2x+(sinx)^2
=(1/2)[1-2(sinx)^2]-(√3/2)sin2x+(sinx)^2
=1/2-(sinx)^2-(√3/2)sin2x+(sinx)^2
=1/2-(√3/2)sin2x.
∴当sin2x=-1时,f(x)有最大值为1/2+√3/2.
当sin2x=1时,有最小值为1/2-√3/2
值域为1/2-√3/2小于y小于1/2+√3/2.
f(x)的最小正周期=2π/2=π.