设sin(x+y)sin(x-y)=m,则cos^2x-cos^2y的值

来源：学生作业帮编辑：搜狗做题网作业帮分类：数学作业时间：2024/08/11 08:58:04

sin(x+y)sin(x-y)=[sinxcosy+sinycosx][sinxcosy-cosxsiny]=(sinxcosy)^2-(cosxsiny)^2
=(1-cos^2y)cos^2y-cos^2x(1-cos^2y)
=cos^2y-cos^2x=m
故cos^2x-cos^2y=-m
再问： (sinxcosy)^2-(cosxsiny)^2怎么到 (1-cos^2y)cos^2y-cos^2x(1-cos^2y)
再答： (sinxcosy)^2-(cosxsiny)^2 =sin^2xcos^2y-cos^2xsin^2y 不好意思我(1-cos^2y)那里写错了应该是(1-cos^2x) 如下 =(1-cos^2x)cos^2y-cos^2x(1-cos^2y) =cos^2y-cos^2x

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