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cos 3A + cos 3B + cos 3C = 1

Source: Polish MO Finals 1952 p4

August 28, 2024
geometrytrigonometry

Problem Statement

Prove that if the angles A A , B B , C C of a triangle satisfy the equation cos⁡3A+cos⁡3B+cos⁡3C=1,\cos 3A + \cos 3B + \cos 3C = 1, then one of these angles equals 120∘120^\circ .
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