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$g(x) = f(x) f(1-x)$

Source: 41-st Vietnamese Mathematical Olympiad 2003

March 10, 2007
functiontrigonometrycalculusalgebra proposedalgebra

Problem Statement

Let f:R→Rf: \mathbb{R}\to\mathbb{R} is a function such that f(cot⁡x)=cos⁡2x+sin⁡2xf( \cot x ) = \cos 2x+\sin 2x for all 0<x<π0 < x < \pi. Define g(x)=f(x)f(1−x)g(x) = f(x) f(1-x) for −1≤x≤1-1 \leq x \leq 1. Find the maximum and minimum values of gg on the closed interval [−1,1].[-1, 1].
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