International Mathematical Olympiad 1965 Problem 1

AbsAlgebraInequalitiesTrigonometry

Determine all values 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 \left| \sqrt{1 + \sin 2x} - \sqrt{1 - \sin 2x} \right| \leq \sqrt{2}.