f(x)=1/2sin2x-√3cos^2x+√3/2
=1/2sin2x-√3(1+cos2x)/2+√3/2
=1/2sin2x-√3/2cos2x
=sin(2x-π/3)
明显是周期函数 最小正周期T=2π/2=π
f(x+π)=sin(2x+2π-π/3)=sin(2x-π/3)=f(x)