$\{x \in R : \cos 2 x + 2 \cos^{2} x = 2\}$ is equal to

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$\{2 n π + \frac{π}{3} : n \in Z\}$

$\{n π \pm \frac{π}{6} : n \in Z\}$

$\{n π + \frac{π}{3} : n \in Z\}$

$\{2 n π - \frac{π}{3} : n \in Z\}$

answer is B.

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Detailed Solution

We have

$\begin{array}{l} \cos 2 x + 2 \cos^{2} x = 2 \\ \Rightarrow 4 \cos^{2} x = 3 \Rightarrow \cos^{2} x = \cos^{2} \frac{π}{6} \Rightarrow x = n π \pm \frac{π}{6}, n \in Z \end{array}$

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