设(x+y)/2=a,(x-y)/2=b,则sinx-siny=-2/3 ==> 2cosa*sinb=-2/3 --(1);cosx-cosy=2/3 ==> -2sina*sinb=2/3 --(2).由(2)÷(1)并注意到x、y为锐角,即a也是锐角,得tana=1 ==> a=45度,故x+y=2a=90度,即sin(x+y)=sin90=1。

先用公式展开sin(x+y)然后cosx-cosy乘sinx-siny就柳暗花明了!x,y为锐角，0<x+y<180则sin(x+y)的值应该为正自己算算看

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