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sin x + sin (m x) >= 1.8 - VI Soros Olympiad 1999-00 Round 1 10.9

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May 21, 2024
algebratrigonometryinequalities

Problem Statement

Prove that for any λ>3\lambda > 3 there is a number xx for which sin⁡x+sin⁡(λx)≥1.8.\sin x + \sin (\lambda x) \ge 1.8.
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