Show that the equation has no solution for

MATHEMATICS · Subjective · AoPS · Mathematics · Special Functions · Special Functions

Problem

Show that the equation sin⁡x=[1+sin⁡x]+[1−cos⁡x]\sin x=[1+\sin x]+[1-\cos x] has no solution for x∈Rx\in\mathbb{R}, where [ ⋅ ][\,\cdot\,] represents the greatest integer function.

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