\(\bf 2cos(4x)-1=0\implies 2cos(4x)=1\implies cos(4x)=\cfrac{1}{2}
\\\\\\
cos^{-1}\left[ cos(4x) \right]=cos^{-1}\left[ \cfrac{1}{2} \right]\implies
4x=cos^{-1}\left( \cfrac{1}{2} \right)
\\\\\\
\measuredangle x = \cfrac{cos^{-1}\left( \frac{1}{2} \right)}{4}\)
check your Unit Circle for all angles on that range that have a cosine of 1/2
then divide that by 4... for example hmmmm say \(\bf \frac{\pi }{3}\) is one, thus x = \(\bf \cfrac{\frac{\pi }{3}}{4}\implies \cfrac{\pi }{3}\cdot \cfrac{1}{4}\implies \cfrac{\pi }{12}\)
that's one
