f(x)=2sinx/2cosx/2-2√3sinx/4+√3
=sinx/2-2√3[1-cosx/2)/2]+√3
=sinx/2-√3+√3cosx/2+√3
=sinx/2+√3cos2x
=2sin(x/2+π/3)
所以最小正周期T=2π/(1/2)=4π