·求一道数学题的解题过程

f(x)
=2cosxsin(x+π/3)-√3/2
=cosx(sinxcosπ/3+cosxsinπ/3)-√3/2
=1/2sinxcosx+√3/2cosxcosx-√3/2
=1/4sin2x+√3/4cos2x-√3/4
=1/2sin(2x+π/3)-√3/4
∴最小正周期：
T=2π/2=π

看图吧