你公式没背好,sin(x-y)=sin(x+(-y))=sinxcos(-y)+cosxsin(-y),sinx为奇函数,cosx为偶函数,所以
cos(-y)=cosy,sin(-y)=-siny,所以sin(x-y)=sinxcosy-cosxsiny,这里
-cos（π/6）sinx+sin（π/6）cosx=sin（π/6）cosx-cos（π/6）sinx,对照上面我推倒的公式可以看出结果为sin（π/6-x）.
另外根据你说的辅助角的cosθ=-√3/2,sinθ=1/2 θ应该为5π/6+2kπ,-π/6的正弦为-1/2,不是1/2