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sin^2 a + sin^2 b >=sin a sin b+ sin a+ sinb -1

Source: Polish MO Finals 1955 p4

August 29, 2024
trigonometryinequalitiesalgebra

Problem Statement

Prove that sin⁡2α+sin⁡2β≥sin⁡αsin⁡β+sin⁡α+sin⁡β−1. \sin^2 \alpha + \sin^2 \beta \geq \sin \alpha \sin \beta + \sin \alpha + \sin \beta - 1.
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