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ASU 311 All Soviet Union MO 1981 acos(x)+b cos(3x)<=1 =>|b|\le 1

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July 23, 2019
inequalitiestrigonometryalgebra

Problem Statement

It is known about real aa and bb that the inequality acos⁡x+bcos⁡(3x)>1a \cos x + b \cos (3x) > 1 has no real solutions. Prove that ∣b∣≤1|b|\le 1.
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