Determinant left| {begin{array}{*{20}{c}}{cos ,,(θ , + ,phi )}&{ - ,sin ,,(θ , + ,phi )}&{

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3 and 4 .Determinants and Matrices

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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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