Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 4.8 AIME Find the answer

4. Given that $\alpha$ is an acute angle, $\beta$ is an obtuse angle, and $\sec (\alpha-$ $2 \beta)$ , $\sec \alpha$ , $\sec (\alpha+2 \beta)$ form an arithmetic sequence. Then the value of $\frac{\cos \alpha}{\cos \beta}$ is $\qquad$ .

Your answer

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

Solution

4. $-\sqrt{2}$

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