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a cos x + b cos 2x <= 0 (V Soros Olympiad 1998-99 Round 1 11.3)

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May 25, 2024
algebrainequalitiestrigonometry

Problem Statement

For what a from the interval [0,π][0,\pi] do there exist aa and bb that are not simultaneously equal to zero, for which the inequality acos⁡x+bcos⁡2x≤0a \cos x + b \cos 2x \le 0 is satisfied for all xx belonging to the segment [a,π][a, \pi]?
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