因f(x)=sinx(cosx-√3sinx)
=sinxcosx-√3(sinx)^2
=1/2sin2x-√3[(1-cos2x)/2]
=1/2sin2x+√3/2cos2x-√3
=(cosπ/3sin2x+sinπ/3cos2x)-√3
=sin(2x+π/3)-√3
则T+min=2π/2=π