Gujarati
Hindi
3 and 4 .Determinants and Matrices
normal

The determinant $\left| {\begin{array}{*{20}{c}}{\cos \,\,(\theta \, + \,\phi )}&{ - \,\sin \,\,(\theta \, + \,\phi )}&{\cos \,2\phi }\\{\sin \,\theta }&{\cos \,\theta }&{\sin \,\phi }\\{ - \,\cos \,\theta }&{\sin \,\theta }&{\cos \,\phi }\end{array}} \right|$ is :

A$0$
Bindependent of $\theta$
Cindependent of $\phi$
Dindependent of $\theta \, \& \, \phi$ both

Solution

Directly open by $R_1$ to get $Cos^2(\theta + \phi ) + sin^2 (\theta + \phi ) + \cos2 \phi = 1 + cos2\phi$.
Which is independent of $\theta$
Standard 12
Mathematics

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