![cos^2 x-cos^2(4x)<0](https://tex.z-dn.net/?f=cos%5E2+x-cos%5E2%284x%29%3C0)
![\frac{1+cos(2x))}{2}-\frac{1+cos(8x)}{2}<0](https://tex.z-dn.net/?f=%5Cfrac%7B1%2Bcos%282x%29%29%7D%7B2%7D-%5Cfrac%7B1%2Bcos%288x%29%7D%7B2%7D%3C0)
![cos(2x)-cos(8x)<0](https://tex.z-dn.net/?f=cos%282x%29-cos%288x%29%3C0)
![-2sin\frac{2x-8x}{2}sin\frac{2x+8x}{2}<0](https://tex.z-dn.net/?f=-2sin%5Cfrac%7B2x-8x%7D%7B2%7Dsin%5Cfrac%7B2x%2B8x%7D%7B2%7D%3C0)
![sin(3x)sin(5x)<0](https://tex.z-dn.net/?f=sin%283x%29sin%285x%29%3C0)
![sin (3x)>0;sin(5x)<0](https://tex.z-dn.net/?f=sin+%283x%29%3E0%3Bsin%285x%29%3C0)
либо
![sin(3x)<0;sin(5x)>0](https://tex.z-dn.net/?f=sin%283x%29%3C0%3Bsin%285x%29%3E0)
первый случай
![2*\pi*k<3x<\pi+2*\pi*k;\pi+2*\pi*n<5x<2*\pi+2*\pi*n](https://tex.z-dn.net/?f=2%2A%5Cpi%2Ak%3C3x%3C%5Cpi%2B2%2A%5Cpi%2Ak%3B%5Cpi%2B2%2A%5Cpi%2An%3C5x%3C2%2A%5Cpi%2B2%2A%5Cpi%2An)
![\frac{2*\pi*k}{3}<x<\frac{\pi}{3}+\frac{2*pi}{3};\\\\\frac{\pi}{5}+\frac{2*\pi}{5}<x<\frac{2*\pi}{5}+\frac{2*\pi*n}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B2%2A%5Cpi%2Ak%7D%7B3%7D%3Cx%3C%5Cfrac%7B%5Cpi%7D%7B3%7D%2B%5Cfrac%7B2%2Api%7D%7B3%7D%3B%5C%5C%5C%5C%5Cfrac%7B%5Cpi%7D%7B5%7D%2B%5Cfrac%7B2%2A%5Cpi%7D%7B5%7D%3Cx%3C%5Cfrac%7B2%2A%5Cpi%7D%7B5%7D%2B%5Cfrac%7B2%2A%5Cpi%2An%7D%7B5%7D)
0-60, 120-180, 240-300
36-72, 108-144, 180-216, 252-290, 324-360
общее
![(\frac{\pi}{5}+2*\pi*k;\frac{\pi}{3}+2*\pi*k) \cup \\\\(\frac{2*\pi}{3}+2*\pi*k;\frac{4*\pi}{5}+2*\pi*k) \cup \\\\ (\frac{7*\pi}{5}+2*\pi*k;\frac{9*\pi}{5}+2\pi*k](https://tex.z-dn.net/?f=%28%5Cfrac%7B%5Cpi%7D%7B5%7D%2B2%2A%5Cpi%2Ak%3B%5Cfrac%7B%5Cpi%7D%7B3%7D%2B2%2A%5Cpi%2Ak%29+%5Ccup+%5C%5C%5C%5C%28%5Cfrac%7B2%2A%5Cpi%7D%7B3%7D%2B2%2A%5Cpi%2Ak%3B%5Cfrac%7B4%2A%5Cpi%7D%7B5%7D%2B2%2A%5Cpi%2Ak%29+%5Ccup+%5C%5C%5C%5C+%28%5Cfrac%7B7%2A%5Cpi%7D%7B5%7D%2B2%2A%5Cpi%2Ak%3B%5Cfrac%7B9%2A%5Cpi%7D%7B5%7D%2B2%5Cpi%2Ak)
[36-60][120-144][252-290]
по второму
60-120, 180-240, 300-420
72-108, 144-180, 216-252, 290-324, 360-412
[72-108][216-240][300-324][360-412]
![(\frac{2*\pi}{5}+2*\pi*k;\frac{3*\pi}{5}+2*\pi*k) \cup \\\\(\frac{6*\pi}{5}+2*\pi*k;\frac{7*\pi}{5}) \cup \\\\(\frac{5*\pi}{3}+2*\pi*k;\frac{9*\pi}{5}+2*\pi*k) \cup \\\\(2*\pi+2*\pi*k;\frac{12*\pi}{5}+2*\pi*k](https://tex.z-dn.net/?f=%28%5Cfrac%7B2%2A%5Cpi%7D%7B5%7D%2B2%2A%5Cpi%2Ak%3B%5Cfrac%7B3%2A%5Cpi%7D%7B5%7D%2B2%2A%5Cpi%2Ak%29+%5Ccup+%5C%5C%5C%5C%28%5Cfrac%7B6%2A%5Cpi%7D%7B5%7D%2B2%2A%5Cpi%2Ak%3B%5Cfrac%7B7%2A%5Cpi%7D%7B5%7D%29+%5Ccup+%5C%5C%5C%5C%28%5Cfrac%7B5%2A%5Cpi%7D%7B3%7D%2B2%2A%5Cpi%2Ak%3B%5Cfrac%7B9%2A%5Cpi%7D%7B5%7D%2B2%2A%5Cpi%2Ak%29+%5Ccup+%5C%5C%5C%5C%282%2A%5Cpi%2B2%2A%5Cpi%2Ak%3B%5Cfrac%7B12%2A%5Cpi%7D%7B5%7D%2B2%2A%5Cpi%2Ak)
k є Z
обьединяем решение первого и второго случая получаем ответ