A) \[\frac{2{{\sin }^{2}}2\theta }{\sin \theta }\]
B) \[8{{\cos }^{3}}\theta -4\cos \theta +6\]
C) \[\frac{2\sin 2\theta }{\sin \theta }\]
D) \[8{{\cos }^{3}}\theta +4\cos \theta +6\]
Correct Answer: B
Solution :
[b] Given that, \[\Delta =\left[ \begin{matrix} C & 1 & 0 \\ 1 & C & 1 \\ 6 & 1 & C \\ \end{matrix} \right]=C({{C}^{2}}-1)-1(C-6)\] \[\Rightarrow \,\,\Delta =2\cos \theta (4{{\cos }^{2}}\theta -1)-(2\cos \theta -6)\] \[(\because \,\,\,\,C=2\cos \theta \,\,given)\] \[=8{{\cos }^{3}}\theta -4\cos \theta +6\]
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