运用倍角公式有
f(x)=sinxcosx+√3cos²x-√3/2
=(1/2)sin2x+(√3/2)(1+cos2x)-√3/2
=(1/2)sin2x+(√3/2)cos2x
=sin2xcos(π/3) +cos2xsin(π/3)
=sin[2x+(π/3)]
最小正周期=2π/2=π