已知sin(x+y)=2/3,sin(x-y)=2/5,则tanx/tany的值是多少?
问题描述:
已知sin(x+y)=2/3,sin(x-y)=2/5,则tanx/tany的值是多少?
答
Sin(x+y)=sinxcosy+cosxsiny=2/3,
sin(x-y)=sinxcosy-cosxsiny=2/5得
两式相加的sinxcosy=8/15
两式相减的cosxsiny=2/15
然后再一比可得sinxcosy/cosxsiny=tanx/tany=4