Prove that the determinant \( \left|\begin{array}{ccc}x & \sin \the...

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Prove that the determinant \( \left|\begin{array}{ccc}x & \sin \theta & \cos \theta \\ -\sin \theta & -x & 1 \\ \cos \theta & 1 & x\end{array}\right| \) is independent of \( \theta \).
\( \mathrm{P} \)
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