f(x)=2cosxsin(x+π/3)-√3/2
=2cosx[sinx*(1/2)+cosx(√3/2）]-√3/2
=sinxcosx+√3cos^2 x-√3/2
=(1/2)sin(2x)+(1/2)cos(2x)
=(√2/2)sin(2x+π/4)
∴最小正周期是T=2π/2=π