If denotes the greatest integer less than or equal to

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

If [x][x] denotes the greatest integer less than or equal to xx, then the equation sin⁡x=[1+sin⁡x]+[1−cos⁡x]\sin x=[1+\sin x]+[1-\cos x] has no solution in (1) [−π2,π2]\left[-\frac{\pi}{2},\frac{\pi}{2}\right] (2) [π2,π]\left[\frac{\pi}{2},\pi\right] (3) [π,3π2]\left[\pi,\frac{3\pi}{2}\right] (4) R\mathbb{R}

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