A) \[\frac{\sin 4\theta }{\sin \theta }\]
B) \[\frac{2{{\sin }^{2}}2\theta }{\sin \theta }\]
C) \[4{{\cos }^{2}}\theta (2cos\theta -1)\]
D) None of the above
Correct Answer: D
Solution :
Let \[\Delta =\left| \begin{matrix} C & 1 & 0 \\ 1 & C & 1 \\ 6 & 1 & C \\ \end{matrix} \right|=C({{C}^{2}}-1)-1(C-6)\] \[{{C}^{3}}-2C+6\] Put \[C=2\cos \theta ,\]we get \[\Delta ={{(2\cos \theta )}^{3}}-2(cos\theta )+6\] \[=8{{\cos }^{3}}\theta -4\cos \theta +6\]
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