Question 3
Let $a_0,a_1,\ldots,a_n\in(0,\pi/2)$ satisfy
\[\sum_{i=0}^n\tan(a_i-\pi/4)\ge n-1.\]
Prove that $\prod_{i=0}^n\tan a_i\ge n^{n+1}$.
\[\sum_{i=0}^n\tan(a_i-\pi/4)\ge n-1.\]
Prove that $\prod_{i=0}^n\tan a_i\ge n^{n+1}$.
USAMO 1998 — Days 1 and 2 Question 3
USAMO · USAMO 1998 — Days 1 and 2