文[1]利用组合数的性质等知识解决了函数f(x)=a/cos~nx+b/sin~nx(0xπ/2,a,b为大于0的常数,n∈N*)的最小值问题,但解题过程较为复杂.笔者经过探索,找到一种较为简单的解法,供参考.引理1若a,b,x,y都是正实数,n为大于1的正整数,则axn+byn≥((aax++b)byn-)1n,1当且仅当x=y时,取 The paper [1] uses knowledge of the properties of the combination number to solve the function f(x)=a/cos~nx+b/sin~nx (0xπ/2, a, b is a constant greater than 0, n∈N*) The problem of minimum value, but the problem-solving process is more complicated. The author has explored and found a relatively simple solution for reference. Lemma 1 If a, b, x, y are all positive real numbers, n is a positive integer greater than 1, then Axn+byn≥((aax++b)byn-)1n,1 if and only if x=y