已知A,B都是锐角,且A+B不=派/2.(1+tanA)(1+tanB)=2,求证A+B=派/4.写过程!万分感激!急需!
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![已知A,B都是锐角,且A+B不=派/2.(1+tanA)(1+tanB)=2,求证A+B=派/4.写过程!万分感激!急需!](/uploads/image/z/2678766-6-6.jpg?t=%E5%B7%B2%E7%9F%A5A%2CB%E9%83%BD%E6%98%AF%E9%94%90%E8%A7%92%2C%E4%B8%94A%2BB%E4%B8%8D%3D%E6%B4%BE%2F2.%281%2BtanA%29%281%2BtanB%29%3D2%2C%E6%B1%82%E8%AF%81A%2BB%3D%E6%B4%BE%2F4.%E5%86%99%E8%BF%87%E7%A8%8B%21%E4%B8%87%E5%88%86%E6%84%9F%E6%BF%80%21%E6%80%A5%E9%9C%80%21)
已知A,B都是锐角,且A+B不=派/2.(1+tanA)(1+tanB)=2,求证A+B=派/4.写过程!万分感激!急需!
已知A,B都是锐角,且A+B不=派/2.(1+tanA)(1+tanB)=2,
求证A+B=派/4.
写过程!万分感激!急需!
已知A,B都是锐角,且A+B不=派/2.(1+tanA)(1+tanB)=2,求证A+B=派/4.写过程!万分感激!急需!
由题意:
(1+tanA)(1+tanB)=2
∴1+tanA+tanB+tanA*tanB=2
∴tanA+tanB=2-1-tanA*tanB
∴tanA+tanB=1-tanA*tanB
∴tan(A+B)
=(tanA+tanB)/(1-tanA*tanB)
=1
∵a、b都是锐角且A+B≠π/2
∴A+B=π/4