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