If \[\sin \beta \]is the geometric mean between \[\sin \alpha \]and \[\cos \alpha ,\]then \[\cos 2\beta \]is equal to

\[2{{\sin }^{2}}\left( \frac{\pi }{4}+\alpha \right)\]

\[2{{\sin }^{2}}\left( \frac{\pi }{4}-\alpha \right)\]

\[2{{\cos }^{2}}\left( \frac{\pi }{4}-\alpha \right)\]

\[2{{\cos }^{2}}\left( \frac{\pi }{4}+\alpha \right)\]

If \[\sin \beta \]is the geometric mean between \[\sin \alpha \]and \[

1.	If \[\sin \beta \]is the geometric mean between \[\sin \alpha \]and \[\cos \alpha ,\]then \[\cos 2\beta \]is equal to
A.	\[2{{\sin }^{2}}\left( \frac{\pi }{4}-\alpha \right)\]
B.	\[2{{\cos }^{2}}\left( \frac{\pi }{4}-\alpha \right)\]
C.	\[2{{\cos }^{2}}\left( \frac{\pi }{4}+\alpha \right)\]
D.	\[2{{\sin }^{2}}\left( \frac{\pi }{4}+\alpha \right)\]
Answer» D. \[2{{\sin }^{2}}\left( \frac{\pi }{4}+\alpha \right)\]

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If \[\sin \beta \]is the geometric mean between \[\sin \alpha \]and \[\cos \alpha ,\]then \[\cos 2\beta \]is equal to

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