f(x)=√3/2 * sin2x-1/2 *(cos^2x-sin^2x)-1
=√3/2 * sin2x-1/2 *cos2x-1
=sin2x*cosπ/6-cos2xsinπ/6-1
=sin(2x-π/6)-1
当sin(2x-π/6)=-1时有最小值
f(x)=-1-1=-2
最小正周期T=2π/2=π