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Inequality with angles

Source: Chinese Northern Mathematical Olympiad 2007

August 5, 2007
inequalitiestrigonometryinequalities proposed

Problem Statement

Let α \alpha, β \beta be acute angles. Find the maximum value of (1−tan⁡αtan⁡β)2cot⁡α+cot⁡β \frac{\left(1-\sqrt{\tan\alpha\tan\beta}\right)^{2}}{\cot\alpha+\cot\beta}
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