(cosx)^2-(cosy)^2=1/3求sin(x+y)*sin(x-y).

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/23 15:36:03

cos²x-cos²y=1/3
sin(x+y)sin(x-y)
=(sinxcosy+cosxsiny)(sinxcosy-cosxsiny)
=sin²xcos²y-cos²xsin²y
=(1-cos²x)cos²y-cos²x(1-cos²y)
=cos²y-cos²xcos²y-cos²x+cos²xcos²y
=cos²y-cos²x
=-1/3
再问：第三行怎么得到的
再答： sin(a+b)=sinacosb+cosasinb sin(a-b)=sinacosb-cosasinb sin(x+y)sin(x-y) =(sinxcosy+cosxsiny)(sinxcosy-cosxsiny) ///这个就是普通的划开 =sin²xcos²y-cos²xsin²y / //这个是平方差公式 a²-b²=(a+b)(a-b)

sinx+siny=-1/3 cosx+cosy=1/2,求sin(x+y)的值. 求证cosx-cosy=-2sin （x+y/2）*sin （x-y/2）已知sinx-siny=1/2,cosx-cosy=1/2,x、y均为锐角,求sin(x-y) sinx+siny=1/2,cosx+cosy=（根号3）/3,求sin[(x-y)/2] 已知sinx+siny=1/3,cosx-cosy=1/5,求cos(x+y),sin(x-y). 证明cosx(cosx-cosy)+sinx(sinx-siny)=2sin(x-y)/2 sinx+siny=√2/2 cosx+cosy=√6/2 求sin(x+y)求解答. 求解一阶微分方程：(3x+2cosy)dx-x sin y d y=0 若cos(x+y)cosy+sin(x+y)siny=0,则cosx= 已知cos(x-y)cosx+sin(x-y)sinx=3/5,则cosy的值为已知cosx+cosy=1/2,sinx-siny=1/3,求cos(x+y) 已知0小于x小于2/π,cosx=3/5,求tanx的值,若2/π小于y小于π且sin(x=y)=5/13,求cosy的