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Trigonometry makes rational number

Source: All-Russian MO 2023 Final stage 11.1

April 23, 2023
trigonometryquadratics

Problem Statement

If x∈Rx\in\mathbb{R} satisfy sinsin x+tanx+tan x∈Qx\in\mathbb{Q}, coscos x+cotx+cot x∈Qx\in\mathbb{Q} Prove that sinsin 2x2x is a root of an integral coefficient quadratic function
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