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x+y+z=0 then |cos x| + |cos y| + |cos z| > 1

Source: Romanian IMO Team Selection Test TST 1988, problem 11

October 1, 2005
trigonometryinequalities proposedinequalities

Problem Statement

Let x,y,zx,y,z be real numbers with x+y+z=0x+y+z=0. Prove that ∣cos⁡x∣+∣cos⁡y∣+∣cos⁡z∣≥1. |\cos x |+ |\cos y| +| \cos z | \geq 1 . Viorel Vajaitu, Bogdan Enescu
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