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Trigonometric inequality for non-obtuse angles

Source: IberoAmerican 1989 Q2

November 27, 2010
inequalitiestrigonometryinequalities proposed

Problem Statement

Let x,y,zx,y,z be real numbers such that 0≤x,y,z≤π20\le x,y,z\le\frac{\pi}{2}. Prove the inequality π2+2sin⁡xcos⁡y+2sin⁡ycos⁡z≥sin⁡2x+sin⁡2y+sin⁡2z.\frac{\pi}{2}+2\sin x\cos y+2\sin y\cos z\ge\sin 2x+\sin 2y+\sin 2z.
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