# 1998 USAMO Problems/Problem 3

1998 USAMO Problem #1

Problem:

Let be real numbers in the interval such that . Prove that .

Solution:

Let , where . Then we have

By AM-GM,

- $\prod_{i = 0}^n{\frac {1 + y_i}{n}}\ge \prod_{i = 0}^n{\prod_{j\neq i}{(1 - y_j)^{\frac {1}{n}}}$ (Error compiling LaTeX. ! Missing } inserted.)

Note that by the addition formula for tangents, .

So , as desired.