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sin n a + sin nb + sin nc < 0 - All-Russian MO 2004 Regional (R4) 11.7

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September 27, 2024
algebrainequalitiestrigonometry

Problem Statement

For what natural numbers nn for any numbers a,b,ca, b , c, which are values of the angles of an acute triangle, the following inequality is true: sin⁡na+sin⁡nb+sin⁡nc<0?\sin na + \sin nb + \sin nc < 0?
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