实数x,y满足tanx=x,tany=y,且绝对值x不等于绝对值y,求sin(x-y)/(x-y)-sin(
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实数x,y满足tanx=x,tany=y,且绝对值x不等于绝对值y,求sin(x-y)/(x-y)-sin(
![实数x,y满足tanx=x,tany=y,且绝对值x不等于绝对值y,求sin(x-y)/(x-y)-sin(](/uploads/image/z/18630095-23-5.jpg?t=%E5%AE%9E%E6%95%B0x%2Cy%E6%BB%A1%E8%B6%B3tanx%3Dx%2Ctany%3Dy%2C%E4%B8%94%E7%BB%9D%E5%AF%B9%E5%80%BCx%E4%B8%8D%E7%AD%89%E4%BA%8E%E7%BB%9D%E5%AF%B9%E5%80%BCy%2C%E6%B1%82sin%EF%BC%88x-y%EF%BC%89%2F%28x-y%EF%BC%89-sin%28)
sinx/cosx=tanx=x
sinx=xcosx
同理
siny=ycosy
所以原式=(sinxcosy-cosxsiny)/(x-y)-(sinxcosy+cosxsiny)/(x+y)
=(xcosxcosy-ycosxcosy)/(x-y)-(xcosxcosy+ycosxcosy)/(x+y)
=cosxcosy(x-y)/(x-y)-cosxcosy(x+y)/(x+y)
=cosxcosy-cosxcosy
=0
sinx=xcosx
同理
siny=ycosy
所以原式=(sinxcosy-cosxsiny)/(x-y)-(sinxcosy+cosxsiny)/(x+y)
=(xcosxcosy-ycosxcosy)/(x-y)-(xcosxcosy+ycosxcosy)/(x+y)
=cosxcosy(x-y)/(x-y)-cosxcosy(x+y)/(x+y)
=cosxcosy-cosxcosy
=0
实数x,y满足tanx=x,tany=y,且|x|≠|y|,则sin(x+y)x+y−sin(x−y)x−y
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