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1 < cos A + cos B + cos C <= 3/2

Source: Polish MO Second Round 1971 p2

September 8, 2024
algebrainequalitiestrigonometry

Problem Statement

Prove that if A,B,C A, B, C are angles of a triangle, then 1<cos⁡A+cos⁡B+cos⁡C≤32. 1 < \cos A + \cos B + \cos C \leq \frac{3}{2}.
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