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cos x^2 + cos y^2 - cos xy < 3

Source: 1983 Swedish Mathematical Competition p2

March 28, 2021
algebrainequalitiestrigonometry

Problem Statement

Show that cos⁡x2+cos⁡y2−cos⁡xy<3 \cos x^2 + \cos y^2 - \cos xy < 3 for reals xx, yy.
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