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《中学数字月刊》1997年第2期上,孙锰老师通过设置参数,巧妙地应用平均值不等式及正、余弦函数的平方关系,求得函数y=Asin~mx+Bcos~nx(A、B>0,m、n∈N,且m、n>2)的最小值,受该文的启发,本文将介绍一些如函数y=A/(sin~mx)+B/(cos~nx)(A、B>0,m、n∈N)的最小值求法.1 当A=B、m=n时,应用二元均值不等式,再结合正弦函数的有界性,可求得函数的最小值.
In the second issue of the Digital Middle School Monthly Issue 1997, Sun Mangan skillfully applied the mean inequality and the square relationship of the positive and cosine functions by setting parameters, and obtained the function y=Asin~mx+Bcos~nx(A, B). > 0, m, n ∈ N, and m, n> 2) The minimum value, inspired by the article, this article will introduce some functions such as y = A / (sin ~ mx) + B / (cos ~ nx) ( A, B> 0, m, n ∈ N) The minimum value of the method. 1 When A = B, m = n, the application of the binary mean inequality, combined with the boundedness of the sine function, the minimum value of the function can be obtained .