Question

Prove that all values of theta: `|(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))|=0`
A. `sin theta`
B. `cos theta`
C. `sin theta cos theta`
D. none of these

Answer 1

Correct Answer - 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`