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

Options

A. `-2sin^(2)((pi)/(4)-alpha)`
B. `-2cos^(2)((pi)/(4)+alpha)`
C. `2sin^(2)((pi)/(4)+alpha)`
D. `2cos^(2)((pi)/(4)-alpha)`

Answer

A, B

Explanation

`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)`