化简sin(x+y)sin(x-y)+cos(x+y)cos(x-y)除了展开,有简便算法么?

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化简sin(x+y)sin(x-y)+cos(x+y)cos(x-y)除了展开,有简便算法么?
化简sin(x+y)sin(x-y)+cos(x+y)cos(x-y)除了展开,有简便算法么?

化简sin(x+y)sin(x-y)+cos(x+y)cos(x-y)除了展开,有简便算法么?
这个很简单啊
cos(a-β)=cosacosβ+sinasinβ
这里就是这样啊,把x+y=a,x-y=β带入
sin(x+y)sin(x-y)+cos(x+y)cos(x-y)=cos[(x+y)-(x-y)]=cos2y


利用 cos(a-b)=cosa*cosb+sina*sinb公式
原式=cos[(x+y)-(x-y)]=cos2y

cos(a-β)=cosacosβ+sinasinβ
把x+y=a,x-y=β带入
sin(x+y)sin(x-y)+cos(x+y)cos(x-y)=cos[(x+y)-(x-y)]=cos2y