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Big number trigonometry

Source: Moscow Olympiad 2018, Grade 11, P9

April 7, 2018
algebranumber theorytrigonometry

Problem Statement

xx and yy are integer 55-digits numbers, such that in the decimal notation, all ten digits are used exactly once. Also tan⁡x−tan⁡y=1+tan⁡xtan⁡y\tan{x}-\tan{y}=1+\tan{x}\tan{y}, where x,yx,y are angles in degrees. Find maximum of xx
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