MathDB
Trigonometric inequality

Source: Baltic Way 2005/2

November 7, 2005
inequalitiestrigonometryalgebra proposedalgebra

Problem Statement

Let α\alpha, β\beta and γ\gamma be three acute angles such that sin⁡α+sin⁡β+sin⁡γ=1\sin \alpha+\sin \beta+\sin \gamma = 1. Show that tan⁡2α+tan⁡2β+tan⁡2γ≥38.\tan^{2}\alpha+\tan^{2}\beta+\tan^{2}\gamma \geq \frac{3}{8}.
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