已知5siny=sin(2x+y),求证:tan(x+y)=3/2tanx

问题描述:

已知5siny=sin(2x+y),求证:tan(x+y)=3/2tanx

sin[(x+y)+x]=5sin[(x+y)-x]
sin(x+y)·cosx+cos(x+y)·sinx=5·sin(x+y)·cosx-5·cos(x+y)·sinx
4·sin(x+y)·cosx=6·cos(x+y)·sinx
两边同除以cos(x+y)·cosx得:2·tan(x+y)=3·tanx