The value of the determinant $\left|\begin{array}{rr}a \cos \theta & a \sin \theta \\ -a \sin \theta & a \cos \theta\end{array}\right|$ is :
Answer & explanation
Correct answer: option 2
$\left|\begin{array}{rr}a \cos \theta & a \sin \theta \\ -a \sin \theta & a \cos \theta\end{array}\right|$
$=(a \cos \theta)(a \cos \theta)-(-a \sin \theta)(a \sin \theta)$
$=a^2 \cos ^2 \theta+a^2 \sin ^2 \theta$
$\Delta=a^2\left(\sin ^2 \theta+\cos ^2 \theta\right)$
as $\sin ^2 \theta+\cos ^2 \theta = 1$
$=a^2$