Q.

If sinβ is geometric mean between sinα and cosα, then cos2β=

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a

2sin2π4−α  or  2cos2π4+α

b

2sin2π3−α  or  2cos2π3+α

c

sin2π4−α  or  cos2π4+α

d

sin2π3−α  or  cos2π3+α

answer is A.

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Detailed Solution

sin2β=sinαcosα,cos2β=1−2sinαcosα=(sinα−cosα)2
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If sinβ is geometric mean between sinα and cosα, then cos2β=