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Prove that the determinant [(x,sintheta,...

Prove that the determinant `[(x,sintheta,costheta),(-sintheta,-x,1),(costheta,1,x)]` is independent of `theta`.

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To prove that the determinant \[ D = \begin{vmatrix} x & \sin \theta & \cos \theta \\ -\sin \theta & -x & 1 \\ \cos \theta & 1 & x \end{vmatrix} \] is independent of \(\theta\), we will calculate the determinant step by step. ...
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