已知sin(a+b)=1/2,sin(a-b)=1/3,求tana/tanb的值

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已知sin(a+b)=1/2,sin(a-b)=1/3,求tana/tanb的值
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已知sin(a+b)=1/2,sin(a-b)=1/3,求tana/tanb的值
已知sin(a+b)=1/2,sin(a-b)=1/3,求tana/tanb的值

已知sin(a+b)=1/2,sin(a-b)=1/3,求tana/tanb的值
由sin(a+b)=sinacosb+cosasinb
sin(a+b)=sinacosb+cosasinb
可知
sinacosb=[sin(a+b)+sin(a-b)]/2=5/24
cosasinb=[sin(a+b)-sin(a-b)]/2=1/24
tana/tanb=sinacosb/cosasinb=5

sinacosb=5/12 sinbcosa=1/12
tana/tanb=sinacosb/cosasinb=5

sin(a+b)=sinacosb+cosasinb=1/2.sin(a－b)=sinacosb－cosasinb=1/3.sinacosb＝5/12，cosasinb＝1/12，tana/tanb=sinacosb/cosasinb=(5/12)/(1/12)=5

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