Cos 2x= √2/2

$$\\cos(2x)=\frac{\sqrt2}{2}=\frac{1}{\sqrt2}\\\\
2x=45, 360-45, 360+45, 720-45, .....\\\\
x=22.5, 180-22.5, 180+22.5, 360-22.5,....\\\\
x=180n\pm 22.5\;degrees \qquad n\in Z$$

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