已知sin(X+Y)=2/3,sin(X-Y)=1/5,求(tanX)/(tanY)的值
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已知sin(X+Y)=2/3,sin(X-Y)=1/5,求(tanX)/(tanY)的值
(tanX)/(tanY)=(sinX/cosX)/(sinY/cosY)
=(sinXcosY)/(cosXsinY)
又sinXcosY=(1/2)[sin(X+Y)+sin(X-Y)]
=(1/2)[(2/3)+(1/5)]
=13/30
cosXsinY=(1/2)[sin(X+Y)-sin(X-Y)]
=(1/2)[(2/3)-(1/5)]
=7/30
代入原式,得
(tanX)/(tanY)=(13/30)/(7/30)=13/7
(供参考)
=(sinXcosY)/(cosXsinY)
又sinXcosY=(1/2)[sin(X+Y)+sin(X-Y)]
=(1/2)[(2/3)+(1/5)]
=13/30
cosXsinY=(1/2)[sin(X+Y)-sin(X-Y)]
=(1/2)[(2/3)-(1/5)]
=7/30
代入原式,得
(tanX)/(tanY)=(13/30)/(7/30)=13/7
(供参考)
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