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The value of the determinant |(sintheta,...

The value of the determinant `|(sintheta, costheta, sin2theta) , (sin(theta+(2pi)/3), cos(theta+(2pi)/3), sin(2theta+(4pi)/3)) , (sin(theta-(2pi)/3), cos(theta-(2pi)/3), sin(2theta-(4pi)/3))|`

A

`sin theta`

B

`cos theta`

C

`sin theta cos theta`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
Applying `R_(2) rarr R_(2) + R_(3)`, we have,
`Delta = |(sin theta,cos theta,sin 2 theta),(- sin theta,- cos theta,- sin 2 theta),(sin (theta - (2pi)/(3)),cos (theta - (2pi)/(3)),sin (2 theta - (4pi)/(3)))|= 0`
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