IMO Shortlist 1965 problem 1


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Determine all values of x in the interval 0 \leq x \leq 2\pi which satisfy the inequality 2 \cos{x} \leq \sqrt{1+\sin{2x}}-\sqrt{1-\sin{2x}} \leq \sqrt{2}.
Source: Međunarodna matematička olimpijada, shortlist 1965