sinx-siny=-2/3 .............(1)cosx-cosy=2/3...............(2)(1)^2+(2)^2得:(sinx)^2+(siny)^2-2sinxsiny+(cosx)^2+(cosy)^2-2cosxcosy=8/92-2cos(x-y)=8/9,cos(x-y)=5/9(1)*(2)得:sinxcosx+sinycosy-sinxcosy-si 展开
sinx-siny=-2/3 .............(1)cosx-cosy=2/3...............(2)(1)^2+(2)^2得:(sinx)^2+(siny)^2-2sinxsiny+(cosx)^2+(cosy)^2-2cosxcosy=8/92-2cos(x-y)=8/9,cos(x-y)=5/9(1)*(2)得:sinxcosx+sinycosy-sinxcosy-sinycosx=-4/9(1/2)[sin2x+sin2y]-[sin(x+y)]=-4/9sin2x+sin2y=sin[(x+y)+(x-y)]+sin[(x+y)-(x-y)]=sin(x+y)cos(x-y)+cos(x+y)sin(x-y)+sin(x+y)cos(x-y)-cos(x+y)sin(x-y)=2sin(x+y)cos(x-y)所以(1/2)[sin2x+sin2y]-[sin(x+y)]=sin(x+y)cos(x-y)-sin(x+y)=-4/9得sin(x+y)=1 收起
