A Minimum Over Triangle Angles

★ 8/10trigonometry Extrema Trigonometric Identities AM-GM inequality

Problem

Let $A, B, C$ be the interior angles of a triangle. Find the minimum value of

m = \frac{1}{\sin^2 A} + \frac{1}{\sin^2 B} + \frac{4}{1 + \sin C}.

Answer

Solution

Difficulty	8/10
Topics	trigonometry, Extrema, Trigonometric Identities, AM-GM, inequality

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