[tex]2cos4x-1=0[/tex]
[tex]2cos4x=1[/tex]
[tex]cos4x=\frac{1}{2}[/tex]
[tex]4x=t[/tex]
[tex]cost=\frac{1}{2}[/tex]
[tex]t=\frac{\pi}{3}+2n\pi[/tex]
[tex]4x=\frac{\pi}{3}+2n\pi[/tex]
[tex]x=\frac{\pi}{12}+\frac{n\pi}{2}[/tex]
or
[tex]t=-\frac{\pi}{3}+2n\pi[/tex]
[tex]4x=-\frac{\pi}{3}+2n\pi[/tex]
[tex]x=-\frac{\pi}{12}+\frac{n\pi}{2}[/tex]
[tex]x=\frac{\pi}{12}+\frac{n\pi}{2},-\frac{\pi}{12}+\frac{n\pi}{2}[/tex]
