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If cos beta is the geometric mean betwee...

If `cos beta` is the geometric mean between `sin alpha` and `cos alpha`, where `0ltalpha,betaltpi//2`. Then `cos 2beta` is equal to

A

`-2sin^(2)((pi)/(4)-alpha)`

B

`-2cos^(2)((pi)/(4)+alpha)`

C

`2sin^(2)((pi)/(4)+alpha)`

D

`2cos^(2)((pi)/(4)-alpha)`

Text Solution

Verified by Experts

The correct Answer is:
A, B
`2 sin alpha cos alpha=2cos^(2)beta`
`sin2alpha=1+cos 2beta`
`therefore cos 2beta=-(1-sin 2alpha)`
`=-(1-cos((pi)/(2)-2a))`
`=-2sin^(2)((pi)/(4)-alpha))`
`=-2cos^(2)((pi)/(4)+alpha)`
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Knowledge Check

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    A
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    B
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    D
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