![image](https://tex.z-dn.net/?f=cos4x-cos%5E2x%3D1%5C%5C%0A2cos%5E22x-1-cos%5E2x%3D1%5C%5C+%0A2%282cos%5E2x-1%29%5E2-cos%5E2x-2%3D0%5C%5C%0Acos%5E2x%3Dt%5C%5C%0A2%282t-1%29%5E2-t-2%3D0%5C%5C%0A2%284t%5E2-4t%2B1%29-t-2%3D0%5C%5C%0A8t%5E2-9t%3D0%5C%5C%0At%288t-9%29%3D0%5C%5C%0At%3D0%5C%5C%0At%3D%5Cfrac%7B9%7D%7B8%7D%3E1%5C%5C%5C%5C%0Acosx%3D0%5C%5C+%0Ax%3D%5Cfrac%7B%5Cpi%7D%7B2%7D%2B%5Cpi%5C%2Ak%0A%0A%0A)
1\\\\
cosx=0\\
x=\frac{\pi}{2}+\pi\*k
" alt="cos4x-cos^2x=1\\
2cos^22x-1-cos^2x=1\\
2(2cos^2x-1)^2-cos^2x-2=0\\
cos^2x=t\\
2(2t-1)^2-t-2=0\\
2(4t^2-4t+1)-t-2=0\\
8t^2-9t=0\\
t(8t-9)=0\\
t=0\\
t=\frac{9}{8}>1\\\\
cosx=0\\
x=\frac{\pi}{2}+\pi\*k
" align="absmiddle" class="latex-formula">