Half-Angle Tangents in an AP

★ 7/10trigonometry AM-GM inequality Triangle Geometry

Problem

In $\triangle ABC$ , the sides opposite $A, B, C$ are $a, b, c$ , and $a + c = 2b$ . Prove that

\tan\frac{A}{2}\cdot\tan\frac{C}{2} \geqslant \tan^2\frac{B}{2}.

Answer

Solution

Difficulty	7/10
Topics	trigonometry, AM-GM, inequality, Triangle Geometry

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