A) \[\Delta =0\]
B) \[\Delta \in (0,\infty )\]
C) \[\Delta \in [-1,2]\]
D) \[\Delta \in [2,4]\]
Correct Answer: D
Solution :
\[\because \] \[\Delta =\left| \begin{matrix} 1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1 \\ \end{matrix} \right|\] \[=1(1+si{{n}^{2}}\theta )-\sin \theta (0)+1(si{{n}^{2}}\theta +1)\] \[=2(1+{{\sin }^{2}}\theta )\] \[\because \] \[0\le {{\sin }^{2}}\theta \le 1\] \[\Rightarrow \] \[1\le 1+{{\sin }^{2}}\theta \le 2\] \[\Rightarrow \] \[2\le 2(1+si{{n}^{2}}\theta )\le 4\] \[\Rightarrow \] \[2\le \Delta \le 4\] \[\therefore \] \[\Delta \in [2,4]\]
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