Question

The determinant $\begin{vmatrix}\cos (\theta+\phi) & -\sin (\theta+\phi) & \cos 2 \phi \\ \sin \theta & \cos \theta & \sin \phi \\ -\cos \theta & \sin \theta & \cos \phi\end{vmatrix}$ is :

• A. 0
• B. independent of $\theta$
• C. independent of $\phi$
• D. independent of $\theta$ \& $\phi$ both

Answer 1

Answer: (B)

Directly open by $R_1$ to get
$\cos ^2(\theta+\phi) +\sin ^2(\theta+\phi)+\cos 2 \phi $
$ =1+\cos 2 \phi . \text { Which is independent of } \theta$