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