The value of the determinant $\begin{vmatrix} cos^2\theta & cos \theta sin \theta & 0\\-sin \theta & cos \theta & 0\\0 & 0 & 1\end{vmatrix}$ is equal to

$cos \, \theta $

The correct answer is Option (2) → $\cos θ$

$\begin{vmatrix} \cos^2\theta & \cos \theta \sin \theta & 0\\-\sin \theta & \cos \theta & 0\\0 & 0 & 1\end{vmatrix}$

expanding along $R_3$

$=\cos^3θ+\cos θ\sin^2θ$

$=\cos θ(\cos^2θ+\sin^2θ)$

$=\cos θ$