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《中学数学教学》2 0 0 3年第 3期有奖解题擂台( 61 )中 ,严复卓老师提出了如下一个三角形不等式 :在△ABC中 ,求证cosA·cosB·cosC≤ ( 1 -cosA ) ( 1 -cosB) ( 1 -cosC) ,等号当且仅当A =B =C =π3 时成立。本文给出上述不等式的两种证明方法。证法一 设A≤B≤C ,则当C为直
In the “Middle School Mathematics Teaching” Issue 3rd Issue of the 3rd Issue of the Tuition Award (61), Yan Fuzhuo proposed the following triangle inequality: In △ABC, verify that cosA·cosB·cosC≤ ( 1 -cosA ) ( 1 -cosB) ( 1 -cosC ), the equal sign holds if and only if A =B =C =π3. In this paper, two proof methods for the above inequality are given. According to the proof method, if A≤B≤C, then C is straight.