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If $x+\frac{1}{x}=2 \cos \theta$, then $x$ is equal to
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The correct answer is:
$\cos \theta \pm i \sin \theta$
$\begin{aligned} & x+\frac{1}{x}=2 \cos \theta \Rightarrow x^2-2 x \cos \theta+1=0 \\ & \Rightarrow x=\frac{2 \cos \theta \pm \sqrt{4 \cos ^2 \theta-4}}{2} \Rightarrow x=\cos \theta \pm i \sin \theta\end{aligned}$
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