IMAC 2008 Problem 3

Let $0 \leq x \leq 2\pi$ . Prove the inequality $\sqrt {\frac {\sin^{2}x}{1 + \cos^{2}x}} + \sqrt {\frac {\cos^{2}x}{1 + \sin^{2}x}}\geq 1$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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