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1/3 <= tan 3a / tan a <= 3 not true

Source: Polish MO Finals 1964 p1

August 30, 2024
inequalitiestrigonometry

Problem Statement

Prove that the inequality 13≤tan⁡3αtan⁡α≤3 \frac{1}{3} \leq \frac{\tan 3\alpha}{\tan \alpha} \leq 3 is not true for any value of α \alpha .
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