f(x)=(12)sin2x＋√3cos²x
=(1/2)sin2x＋(√3/2)[1＋cos2x]
=(1/2)sin2x＋(√3/2)cos2x＋(√3/2)
=sin(2x＋π/3)＋(√3/2)
则最小正周期是2π除以【x的系数】=2π/2=π