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

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

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

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-3tany,tanx=5tany,所以tanx/tany=5