实数x，y满足tanx=x，tany=y，且|x|≠|y|，则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|x|≠|y|，则
−sin(x+y) x+y
=______． sin(x−y) x−y
答
tanx=
=xsinx cosx
∴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
故答案为：0