If $\cos 2x =(\sqrt 2 +1) \bigg(\cos x - \large\frac{1}{\sqrt 2}\bigg), \cos x \neq \large\frac{1}{2}$ then $x \in :$

Question

$$\begin {array} {1 1} (a)\;\{ 2n \pi \pm \frac{\pi}{3}:n \in Z \} & \quad (b)\;\{ 2n \pi \pm \frac{\pi}{6}:n \in Z \} \\ (c)\;\{ 2n \pi \pm \frac{\pi}{2}:n \in Z \} & \quad (d)\;\{2n \pi \pm \frac{\pi}{4}:n \in Z \} \end {array}$$