设sin(x+y)sin(x-y)=m,则cos^2x-cos^2y的值

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设sin(x+y)sin(x-y)=m,则cos^2x-cos^2y的值
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设sin(x+y)sin(x-y)=m,则cos^2x-cos^2y的值
设sin(x+y)sin(x-y)=m,则cos^2x-cos^2y的值

设sin(x+y)sin(x-y)=m,则cos^2x-cos^2y的值
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