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IMO 1965 Problem 1

  • Day 1

Determine all values of xx in the interval 0≤x≤2π0 \leq x \leq 2\pi which satisfy the inequality 2cos⁡x≤1+sin⁡2x−1−sin⁡2x≤2.2 \cos{x} \leq \sqrt{1+\sin{2x}}-\sqrt{1-\sin{2x}} \leq \sqrt{2}.

Dataset text AI-MO AoPS. Quoted with source.

Official text: IMO 1965 official English paper, page 1.

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