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在三角函数的条件不等式中,常见的一种条件是不等式中含有三角形三个内角的函数。这类问题有些实质上是多元函数的条件极值问题,数学刊物上已载文不少。本文试用中学数学知识给出几个定理加以解答。定理1 如果锐角α_1和α_2之和为定值A,那末下列不等式成立① sinα_1·sinα_2≤sin~2 1/2 A; ② sinα_1+sinα_2≤2sin 1/2 A; ③ cosα_1·cosα_2≤cos~2 1/2 A; ④ cosα_1+cosα_2≤2cos 1/2 A;
In the conditional inequality of a trigonometric function, a common condition is that the inequality contains a function of three internal angles of a triangle. Some of these problems are essentially conditional extremum problems of multivariate functions. There are many articles in the mathematics publications. This paper tries the middle school mathematics knowledge to give a few theorems to answer. Theorem 1 If the sum of the acute angles α_1 and α_2 is the fixed value A, then the following inequality holds: 1 sinα_1·sinα_2≤sin~2 1/2 A; 2 sinα_1+sinα_2≤2sin 1/2 A; 3 cosα_1·cosα_2≤cos~2 1/2 A; 4 cosα_1+cosα_2≤2cos 1/2 A;