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BG-MO 1965 Problem 2

    Prove the inequality: (1+sin⁡2α)n+(1+cos⁡2α)n≥2(32)n(1+\sin^2\alpha)^n+(1+\cos^2\alpha)^n\ge2\left(\frac32\right)^n is true for every natural number nn . When does equality hold?

    Dataset text AI-MO AoPS. Quoted with source.

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