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xcos x <= pi^2/ 16 if x \in [0, \pi/2]

Source: All-Russian MO 2009 Regional 11. 3

August 28, 2024

algebrainequalitiestrigonometry

Problem Statement

Prove that

x\cos x \le \frac{\pi^2}{16}

for

0 \le x \le \frac{\pi}{2}