If \( \alpha \) and \( \beta \) are acute angles satisfying \( \cos 2 \alpha=\frac{3 \cos 2 \bet...
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If \( \alpha \) and \( \beta \) are acute angles satisfying \( \cos 2 \alpha=\frac{3 \cos 2 \beta-1}{3-\cos 2 \beta} \), then \( \tan \alpha= \)
(A) \( \sqrt{2} \tan \beta \)
(B) \( \frac{1}{\sqrt{2}} \tan \beta \)
(C) \( \sqrt{2} \cot \beta \)
(D) \( \frac{1}{\sqrt{2}} \cot \beta \)
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