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正余弦函数值的有界性,常常用来来计算有关极值的问题,这是一般学生比较熟悉的。但是同学们却常常忽略这个性质在解决其它有关数学问题中的应用,以至有的问题束手无策,或方法不当不能正确、简洁的解答。试举数例说明: 例一.在△ABC中,若2cosA+cosB+cosC=2。求证:A≤π/3。证明:由题设:
The boundedness of the sine and cosine function value is often used to calculate the problem of extreme values, which is familiar to the average student. However, the students often overlook the application of this property in solving other related mathematical problems, and even some problems are incapable, or improper methods can not be correct and concise solutions. Here are a few examples to illustrate: Example 1. In △ABC, if 2cosA+cosB+cosC=2. Proof: A ≤ π/3. Proof: From the question: