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sin 2a> sin 2b> sin 2c if a<b<c in acute ABC

Source: Eotvos 1932 p3

September 10, 2024
trigonometrygeometryinequalities

Problem Statement

Let α\alpha, β\beta and γ\gamma be the interior angles of an acute triangle. Prove that if α<β<γ\alpha < \beta < \gamma then \sin 2\alpha >\ sin 2 \beta > \sin 2\gamma.
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