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(x+y)/(x+y)

问题描述:

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(x+y)/(x+y)

sinx/cosx=tanx=xsinx=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)=cos...