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ASU 451 All Soviet Union MO 1987 cos a, cos 2a, cos 4a, ... , cos((2^n)a)<0

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August 7, 2019
trigonometryalgebra

Problem Statement

Prove such aa, that all the numbers cos⁡a,cos⁡2a,cos⁡4a,...,cos⁡(2na)\cos a, \cos 2a, \cos 4a, ... , \cos (2^na) are negative.
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