A) x only
B) \[\theta \] only
C) x and \[\theta \] both
D) None of these
Correct Answer: B
Solution :
[b] \[\left| \begin{matrix} x & \sin \theta & \cos \theta \\ -\sin \theta & -x & 1 \\ \cos \theta & 1 & x \\ \end{matrix} \right|\] \[=x({{x}^{2}}-1)-\sin \theta (-x\sin \theta -\cos \theta )\] \[+\cos \theta (-\sin \theta +x\cos \theta )\] \[=-{{x}^{3}}-x+x{{\sin }^{2}}\theta +\sin \theta \cos \theta \] \[-\cos \theta \sin \theta +x{{\cos }^{2}}\theta )\] \[={{x}^{3}}-x+x={{x}^{3}}\]
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