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If |(1+sin^2 theta,sin^2 theta,sin^2 the...

If `|(1+sin^2 theta,sin^2 theta,sin^2 theta),(cos^2 theta,1+cos^2 theta,cos^2 theta),(4sin 4 theta,4sin4theta,1+4sin4theta)|=0,` then ...`sin 4theta` equal to ....

A

`1//2`

B

1

C

`-1//2`

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
C
`|{:(,1+sin^(2)theta,sin^(2)theta,sin^(2)theta),(,cos^(2)theta,1+cos^(2)theta,cos^(2)theta),(,4 sin 4theta,4 sin 4theta,1+4 sin 4 theta):}|=0"`
We get `|{:(,1,0,sin^(2)theta),(,-1,1,cos^(2) theta),(,0,-1,1+4 sin 4theta):}|=0 rArr 2(1+2 sin 4 theta)=0 rArr sin 4theta=(-1)/(2)`
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