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cosA+cosB+cosC<=\sqrt5 All-Russian MO 1995 Regional (R4) 11.5

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August 26, 2024
algebrainequalitiestrigonometry

Problem Statement

Angles α,β,γ\alpha, \beta, \gamma satisfy the inequality sin⁡α+sin⁡β+sin⁡γ≥2\sin \alpha +\sin \beta +\sin \gamma \ge 2. Prove that cos⁡α+cos⁡β+cos⁡γ≤5.\cos \alpha + \cos \beta +\cos \gamma \le \sqrt5.
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