MathDB

This might be Jensen!!

Source: Tournament of Towns, Fall 2002, Senior O Level, P4

May 17, 2014

inequalitiestrigonometryinequalities proposed

Problem Statement

x,y,z\in\left(0,\frac{\pi}{2}\right)

are given. Prove that:

\frac{x\cos x+y\cos y+z\cos z}{x+y+z}\le \frac{\cos x+\cos y+\cos z}{3}