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If \( \sin \beta \) is the GM between \( \sin \alpha \) and \( \cos \alpha \), then \( \cos 2 \beta= \)
(A) \( 2 \sin ^{2}\left(\frac{3 \pi}{4}-\alpha\right) \)
(B) \( \cos ^{2}\left(\frac{\pi}{4}+\alpha\right) \)
(C) \( 2 \cos ^{2}\left(\frac{\pi}{4}-\alpha\right) \)
(D) \( 2 \sin ^{2}\left(\frac{\pi}{4}+\alpha\right) \)
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