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cos and sin

Source: All-Russian 2007

May 4, 2007
trigonometryfunctioninequalitiesinequalities unsolved

Problem Statement

Prove that for k>10k>10 Nazar may replace in the following product some one cos⁡\cos by sin⁡\sin so that the new function f1(x)f_{1}(x) would satisfy inequality ∣f1(x)∣≤3⋅2−1−k|f_{1}(x)|\le 3\cdot 2^{-1-k} for all real xx. f(x)=cos⁡xcos⁡2xcos⁡3x…cos⁡2kxf(x) = \cos x \cos 2x \cos 3x \dots \cos 2^{k}x N. Agakhanov
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