I am trying to derive the general solution for the equation $$ 2 \cos^2 x = 1$$
It's get reduced to $$ \cos x = \pm \frac1 {\sqrt{2}} $$
Now, for, $\cos x = \frac 1 {\sqrt{2}} \Rightarrow x = 2n\pi \pm \frac{\pi}{4}$ and for $\cos x = - \frac 1 {\sqrt{2}} \Rightarrow x = 2n\pi \pm \frac{3\pi}{4}$, but I am stuck here I want to know how to derive the general solution that will satisfy the mother equation ($ 2 \cos^2 x = 1$) itself?