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sin x + 1/2 sin 2x + 1/3 sin 3x > 0$

Source: 1949 Hungary - Kürschák Competition p1

October 9, 2022
inequalitiesalgebratrigonometry

Problem Statement

Prove that sin⁡x+12sin⁡2x+13sin⁡3x>0\sin x + \frac12 \sin 2x + \frac13 \sin 3x > 0 for 0<x<180o0 < x < 180^o.
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