若sin(x+y)=1/2,sin(x-y)=1/3,则tanx/tany等于?

问题描述:

若sin(x+y)=1/2,sin(x-y)=1/3,则tanx/tany等于?

sin(x+y)=sinxcosy+cosxsiny=1/2,sin(x-y)=sinxcosy-cosxsiny=1/3,两式作商得(sinxcosy+cosxsiny)/(sinxcosy-cosxsiny)=3/2,分子分母同时除以cosxcosy得(tanx+tany)/(tanx-tany)=3/2,所以2tanx+2tany=3tanx-3tan...