The determinant \[ \left|\begin{array}{ccc} \cos (\theta+\varphi) & -\sin (\theta+\varphi) & \co...

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The determinant
\[
\left|\begin{array}{ccc}
\cos (\theta+\varphi) & -\sin (\theta+\varphi) & \cos 2 \varphi \\
\sin \theta & \cos \theta & \sin \varphi \\
-\cos \theta & \sin \theta & \cos \varphi
\end{array}\right|
\]
is:
\( \mathrm{P} \)
W
(1) 0
(2) independent of \( \theta \)
(3) independent of \( \phi \)
(4) independent of \( \theta \& \phi \) both
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