证明：原式可化为sin(x+π/3)+2sin(x-π/3)-√3cos(2π/3-x)=0左边=1/2×sinx+√3/2×cosx+sinx-√3cosx-√3(-1/2×cosx+√3/2×sinx)=(1/2+1-3/2)sinx+(√3/2-√3+√3/2)cosx=0+0=0=右边∴原等式成立...