question_answer

If \[C=2\,\,cos\,\,\theta ,\] then the value of the determinant \[\Delta =\left| \begin{matrix}    C & 1 & 0  \\    1 & C & 1  \\    0 & 1 & C  \\ \end{matrix} \right|\]  is_______.

A)  \[\frac{\sin 4\theta }{\sin \theta }\]          

B)  \[\frac{2{{\sin }^{2}}2\theta }{\sin \theta }\]

C)  \[4\cos \theta .\cos 3\theta \]       

D)  \[4{{\cos }^{2}}\theta (2\cos \theta -1)\]

E)  None of these