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cos(a),cos(2a),cos(4a),... negative

Source: Croatian MO 2004 4th Grade P4

April 9, 2021
trigonometryalgebra

Problem Statement

Determine all real numbers α\alpha with the property that all numbers in the sequence cos⁡α,cos⁡2α,cos⁡22α,…,cos⁡2nα,…\cos\alpha,\cos2\alpha,\cos2^2\alpha,\ldots,\cos2^n\alpha,\ldots are negative.
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