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sin^n(2x) + (sin^n x - cos^n x)^2 <= 1

Source: All-Russian MO 2000

December 30, 2012
inequalitiestrigonometryinequalities unsolved

Problem Statement

Prove the inequality sin⁡n(2x)+(sin⁡nx−cos⁡nx)2≤1. \sin^n (2x) + \left( \sin^n x - \cos^n x \right)^2 \le 1.
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