一道高中数学三角题
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sin(x+y)/(x+y)-sin(x-y)/(x-y)
=(sinxcosy+cosxsiny)(x-y)/(x^2-y^2)-(sinxcosy-cosxsiny)(x+y)/(x^2-y^2)
=(xsinxcosy+xcosxsiny-ysinxcosy-ycosxsiny-xsinxcosy+xcosxsiny-ysinxcosy+ycosxsiny)/(x^2-y^2)
=(2xcosxsiny-2ysinxcosy)/(x^2-y^2)
=(2x(cosx/sinx)sinxsiny-2ysinxsiny(cosy/siny))/(x^2-y^2)
=2sinxsiny(x^2-y^2)/[m(x^2-y^2)]
=2sinxsiny/m
=(sinxcosy+cosxsiny)(x-y)/(x^2-y^2)-(sinxcosy-cosxsiny)(x+y)/(x^2-y^2)
=(xsinxcosy+xcosxsiny-ysinxcosy-ycosxsiny-xsinxcosy+xcosxsiny-ysinxcosy+ycosxsiny)/(x^2-y^2)
=(2xcosxsiny-2ysinxcosy)/(x^2-y^2)
=(2x(cosx/sinx)sinxsiny-2ysinxsiny(cosy/siny))/(x^2-y^2)
=2sinxsiny(x^2-y^2)/[m(x^2-y^2)]
=2sinxsiny/m
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