f(x)=2cosx*sin(x+π/3)-根号3/2 =2cosx(sinxcosπ/3+cosxsinπ/3)-√3/2=2cosx(1/2sinx+√3/2cosx)-√3/2=sinxcosx+√3cos^2x-√3/2=1/2sin2x+√3(1+cos2x)/2-√3/2=1/2sin2x+√3/2cos2x=sin(2x+π/3)