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acute if sin A > cos B, sin B> cos C, sin C > cos A

Source: Russian Regional Olympiad 2010 11.5

August 24, 2024
geometryacutetrigonometryinequalities

Problem Statement

The angles of the triangle α,β,γ\alpha, \beta, \gamma satisfy the inequalities sin⁡α>cos⁡β,sin⁡β>cos⁡γ,sin⁡γ>cos⁡α.\sin \alpha > \cos \beta, \sin \beta > \cos \gamma, \sin \gamma > \cos \alpha. Prove that the trαiangle is acute-angled.
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