Cotangents in an Acute Triangle

★ 7/10trigonometry Trigonometric Identities AM-GM inequality

Problem

In an acute triangle $ABC$ ,

2\sin^2 A + \sin^2 B = 2\sin^2 C.

Find the minimum value of

\frac{1}{\tan A} + \frac{1}{\tan B} + \frac{1}{\tan C}.

Answer

Solution

Difficulty	7/10
Topics	trigonometry, Trigonometric Identities, AM-GM, inequality

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