MathDB

M2712

Part of Kvant 2022

Problems(1)

Trigonometric inequality

Source: Kvant Magazine No. 8 2022 M2712

3/8/2023
Let ABCABC be a triangle, with ∠A=α,∠B=β\angle A=\alpha,\angle B=\beta and ∠C=γ\angle C=\gamma. Prove that ∑cyctan⁡α2tan⁡β2cot⁡γ2⩾3.\sum_{\text{cyc}}\tan \frac{\alpha}{2}\tan\frac{\beta}{2}\cot\frac{\gamma}{2}\geqslant\sqrt{3}.Proposed by R. Regimov (Azerbaijan)
Kvantgeometrytrigonometryinequalities