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AIME 2011a Problem 9

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Suppose xx is in the interval [0,π/2][0, \pi/2] and log⁡24sin⁡x(24cos⁡x)=32\log_{24\sin x} (24\cos x)=\frac{3}{2}. Find 24cot⁡2x24\cot^2 x.

Dataset text AIME 1983 to 2026. Quoted with source.

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