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|cos nb- cos na| <= n^2 |cos b- cos a|,

Source: Polish MO second round 1970 p1

August 28, 2024
trigonometryinequalitiesalgebra

Problem Statement

Prove that ∣cos⁡nβ−cos⁡nα∣≤n2∣cos⁡β−cos⁡α∣, |\cos n\beta - \cos n\alpha| \leq n^2 |\cos \beta - \cos\alpha|, where nn is a natural number . Check for what values of n n , α \alpha , β \beta equality holds.
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