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
Answer & explanation
Correct answer: option 2
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 $R_3$
$=\cos^3θ+\cos θ\sin^2θ$
$=\cos θ(\cos^2θ+\sin^2θ)$
$=\cos θ$