已知函数f(x)=[2sin(x+π/3)+sinx]cosx-√3sin²x,x∈R

f(x)=[2(sinx*1/2+cosx*√3/2)+sinx]cosx-√3sin²x
=(2sinx+√3cosx)cosx-√3sin²x
=2sinxcosx+√3(cos²x-sin²x)
=sin2x-√3cos2x
=2sin(2x-π/3)
T=2π/2=π