sin(x-y)/sin(x+y)=2009/2010,求tanx/tany

题目

sin(x-y)/sin(x+y)=2009/2010,求tanx/tany

答案

sin（x-y）/sin(x+y)=(sinx*cosy-cosx*siny)/(sinx*cosy+cosx*siny) 1
tanx/tany=(sinx/cosx)*(siny/cosy)=(sinx*cosy)/(cosx*siny) 2
1式各项同除cosx*siny=[(sinx*cosy)/(cosx*siny)-1]/[(sinx*cosy)/(cosx*siny)+1] 3
假设z=tanx/tany=(sinx*cosy)/(cosx*siny) 则3式等于 (z-1)/(z+1)=2009/2010 4
求解4式得到 z=tanx/tany=4019