Problem

Source: Chinese Mathematical Olympiad 2003 Problem 3

Tags: inequalities, trigonometry, inequalities proposed



Given a positive integer $n$, find the least $\lambda>0$ such that for any $x_1,\ldots x_n\in \left(0,\frac{\pi}{2}\right)$, the condition $\prod_{i=1}^{n}\tan x_i=2^{\frac{n}{2}}$ implies $\sum_{i=1}^{n}\cos x_i\le\lambda$. Huang Yumin