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If the determinant |(cos2x,sin^2 x,cos ...

If the determinant `|(cos2x,sin^2 x,cos 4x),(sin^2 x,cos 2x,cos^2 x),(cos 4x,cos^2 x,cos 2x)|` is expanded in powers of `sin x`, then the constant term is

A

1

B

0

C

-1

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
`|{:(1-2 sin^(2)x,,sin^(2)x,,1-8 sin^(2)x(1-sin^(2)x)),(sin^(2)x,,1-sin^(2)x,,1-sin^(2)x),(1-8sin^(2)x(1-sin^(2)x),,1-sin^(2)x,,1-sin^(2)x):}|`
The required constant terms is
`|{:(1,,0,,1),(0,,1,,1),(1,,1,,1):}|+|{:(1,,0,,0),(0,,1,,1),(1,,1,,0):}|=1(10 -1)=-1`
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