А) х принадлежит ( -пи\2+пи*n; пи\4+пи*n] n принадлежит z
б)х принадлежит ( пи*n; пи\6+пи*n) n принадлежит z
в) х принадлежит ( -пи\6+пи*n;пи\2+пи*n) n принадлежит z
г) х принадлежит [3пи\4+пи*n; пи+пи*n) n принадлежит z
2)10+(3-х)³=х²(9-х)-17
10+21-9х-9х+3х²-9х+3х²+3х²-х³=х²(9-х)-17
31-27х+9х²-х³=9х²-х³-17
4)11-х²(х+9)=8х-(х+3)³
11-х³-9х²=8х-х³-3х²-3х²-9х-3х²-9х-9х-27
11-х³-9х²=19х-9х²-х³-27
Наверное всё правильно , но я могла ошибиться!)
1)
![\cos^2x+3\sin x-3=0\\ 1 - \sin^2x+3\sin x-3=0\\ - \sin^2x+3\sin x-2=0\\ \sin^2x-3\sin x+2=0\\ \sin x = t\\ t^2-3t+2=0\\ t_1 = 1, t_2=2\\\\ \sin x = 1\\ x = \frac{\pi}{2} + 2\pi n\\\\ \sin x = 2\\ \varnothing](https://tex.z-dn.net/?f=%5Ccos%5E2x%2B3%5Csin+x-3%3D0%5C%5C%0A1+-+%5Csin%5E2x%2B3%5Csin+x-3%3D0%5C%5C%0A+-+%5Csin%5E2x%2B3%5Csin+x-2%3D0%5C%5C%0A+%5Csin%5E2x-3%5Csin+x%2B2%3D0%5C%5C%0A%5Csin+x+%3D+t%5C%5C%0At%5E2-3t%2B2%3D0%5C%5C%0At_1+%3D+1%2C+t_2%3D2%5C%5C%5C%5C%0A%5Csin+x+%3D+1%5C%5C%0Ax+%3D+%5Cfrac%7B%5Cpi%7D%7B2%7D+%2B+2%5Cpi+n%5C%5C%5C%5C%0A%5Csin+x+%3D+2%5C%5C%0A%5Cvarnothing)
2)
![\sin(2\pi-x)-\cos(\frac{3\pi}{2}+x)+1=0\\](https://tex.z-dn.net/?f=%5Csin%282%5Cpi-x%29-%5Ccos%28%5Cfrac%7B3%5Cpi%7D%7B2%7D%2Bx%29%2B1%3D0%5C%5C)
Упростим уравнение через формулы приведения.
![-\sin x-\sin x+1=0\\ -2\sin x+1=0\\ -2\sin x = -1\\ \sin x = \frac12\\\\ x = (-1)^n\frac{\pi}{6} + \pi n\\](https://tex.z-dn.net/?f=-%5Csin+x-%5Csin+x%2B1%3D0%5C%5C%0A-2%5Csin+x%2B1%3D0%5C%5C%0A-2%5Csin+x+%3D+-1%5C%5C%0A%5Csin+x+%3D+%5Cfrac12%5C%5C%5C%5C%0Ax+%3D+%28-1%29%5En%5Cfrac%7B%5Cpi%7D%7B6%7D+%2B+%5Cpi+n%5C%5C)
3)
![5\sin^2 x-2\sin x \cos x + \cos^2x=4\\](https://tex.z-dn.net/?f=5%5Csin%5E2+x-2%5Csin+x+%5Ccos+x+%2B+%5Ccos%5E2x%3D4%5C%5C)
Разделим все на
![\cos x](https://tex.z-dn.net/?f=%5Ccos+x)
![5\tan^2x-2\tan x + 1=4\\ 5\tan^2x-2\tan x -3=0\\ \tan x =t\\ 5t^2-2t-3=0\\ t_1 = 1, t_2 = -\frac{3}{5}\\\\ \tan x = 1\\ x = \frac{\pi}{4} + \pi n\\\\ \tan x = -\frac35\\\\ x = \arctan(-\frac35) + \pi n\\\\ x = -\arctan \frac35 + \pi n](https://tex.z-dn.net/?f=5%5Ctan%5E2x-2%5Ctan+x+%2B+1%3D4%5C%5C%0A5%5Ctan%5E2x-2%5Ctan+x+-3%3D0%5C%5C%0A%5Ctan+x+%3Dt%5C%5C%0A5t%5E2-2t-3%3D0%5C%5C%0At_1+%3D+1%2C+t_2+%3D+-%5Cfrac%7B3%7D%7B5%7D%5C%5C%5C%5C%0A%5Ctan+x+%3D+1%5C%5C%0Ax+%3D+%5Cfrac%7B%5Cpi%7D%7B4%7D+%2B+%5Cpi+n%5C%5C%5C%5C%0A%5Ctan+x+%3D+-%5Cfrac35%5C%5C%5C%5C%0Ax+%3D+%5Carctan%28-%5Cfrac35%29+%2B+%5Cpi+n%5C%5C%5C%5C%0Ax+%3D+-%5Carctan+%5Cfrac35+%2B+%5Cpi+n)