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Source: All Russian2014 Grade 11 Day 1 P1

April 30, 2014
trigonometryalgebra proposedalgebra

Problem Statement

Does there exist positive a∈Ra\in\mathbb{R}, such that ∣cos⁡x∣+∣cos⁡ax∣>sin⁡x+sin⁡ax|\cos x|+|\cos ax| >\sin x +\sin ax for all x∈Rx\in\mathbb{R}?
N. Agakhanov
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