Q.

If cos⁡ β is the geometric mean between sin⁡ α and cos⁡ α, where 0<α, β<π/2, then cos⁡ 2β is equal to

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a

−2sin2⁡π4−α

b

−2cos2⁡π4+α

c

2sin2⁡π4+α

d

2cos2⁡π4−α

answer is A.

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Detailed Solution

2sin⁡αcos⁡α=2cos2⁡βsin⁡2α=1+cos⁡2β∴ cos⁡2β=−(1−sin⁡2α)=−1−cos⁡π2−2α=−2sin2⁡π4−α=−2cos2⁡π4+α

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If cos⁡ β is the geometric mean between sin⁡ α and cos⁡ α, where 0<α, β<π/2, then cos⁡ 2β is equal to