If cosβ is the geometric mean between sin⁡α and cos⁡α where 0<α,β<π/2 then cos2β is equal to

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−2sin2⁡π4−α

−2cos2⁡π4+α

2sin2⁡π4+α

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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