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\sqrt {\sin^{2}x/(1+\cos^{2}x)}+\sqrt {\cos^{2}x/(1 +\sin^{2}x)}>=1

Source: IMAC Arhimede 2008 p3

May 4, 2019
inequalitiestrigonometryTrigonometric inequality

Problem Statement

Let 0≤x≤2π 0 \leq x \leq 2\pi. Prove the inequality sin⁡2x1+cos⁡2x+cos⁡2x1+sin⁡2x≥1 \sqrt {\frac {\sin^{2}x}{1 + \cos^{2}x}} + \sqrt {\frac {\cos^{2}x}{1 + \sin^{2}x}}\geq 1
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