Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 5.6 AIME, harder Find the answer

6. Let $0<\beta<\alpha<\frac{\pi}{2}$ , and $\operatorname{tg} \alpha=2 \operatorname{tg} \beta$ , then the range of $\alpha-\beta$ is $\qquad$ .

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

6. $\left(0, \frac{\pi}{6}\right]$

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