已知A,B为锐角,且Sin(A-B)=1/2.cos(A+B)=1/3.求tanA*tanB的值
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已知A,B为锐角,且Sin(A-B)=1/2.cos(A+B)=1/3.求tanA*tanB的值
![已知A,B为锐角,且Sin(A-B)=1/2.cos(A+B)=1/3.求tanA*tanB的值](/uploads/image/z/16853785-25-5.jpg?t=%E5%B7%B2%E7%9F%A5A%2CB%E4%B8%BA%E9%94%90%E8%A7%92%2C%E4%B8%94Sin%28A-B%29%3D1%2F2.cos%28A%2BB%29%3D1%2F3.%E6%B1%82tanA%2AtanB%E7%9A%84%E5%80%BC)
Sin(A-B)=1/2.cos(A+B)=1/3,A,B为锐角,有cos(A-B)=根号3/2 Sin(A+B)=2根号2/3,则有 SinASinB=1/2[Cos(A+B)-Cos(A-B)]=(2-3根号3)/12 CosACosB=1/2[Cos(A+B)+Cos(A-B)]=(2+3根号3)/12 tanAtanB=SinASinB/CosACosB=(2-3根号3)/(2+3根号3)
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