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1/sina+ 1/sinb \ge 8/( 3+2 cos c)

Source: North Macedonian Mathematical Olympiad 1996 p3

February 12, 2020
trigonometryinequalitiesGeometric Inequalitiesangles

Problem Statement

Prove that if α,β,γ\alpha, \beta, \gamma are angles of a triangle, then 1sin⁡α+1sin⁡β≥83+2 cosγ\frac{1}{\sin \alpha}+ \frac{1}{\sin \beta} \ge \frac{8}{ 3+2 \ cos\gamma} .
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