阿Q吧 > 若A、B是三角形ABC的内角，并且（1+tanA）（1+tanB）=2

若A、B是三角形ABC的内角，并且（1+tanA）（1+tanB）=2

则A+B等于？p7为什么不是225度呢
2025-03-15 23:59:51
推荐回答（5个）
回答1：

标准答案是45度！
不可能是225度，因为A、B是三角形的内角，所以A+B〈180度。

回答2：

45度

回答3：

1+tanB+tanA+tanAtanB=2 tanA+tanB=1-tanAtanB
tan(A+B)=tanA+tanB/1-tanAtanB
所以tan(A+B)=1
A+B=45度

回答4：

45du

回答5：

由2=(1+tanA)(1+tanB)
=1+tanA+tanB+tanAtanB
得tanA+tanB=1-tanAtanB
故tan(A+B)=(tanA+tanB)/(1-tanAtanB)=1
从而A+B=45°。

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