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cos \alpha + \cos\beta + \cos\beta <= \frac{3}{2}

Source: Germany 1965 p6

February 21, 2020
trigonometryinequalitiesGeometric Inequalitiesgeometry

Problem Statement

Let α,β,γ\alpha,\beta, \gamma be the angles of a triangle. Prove that cos⁡α,+cos⁡β+cos⁡γ≤32\cos\alpha, + \cos\beta + \cos\gamma \le \frac{3}{2} and find the cases of equality.
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