![\sin^2x+\cos^22x-(\sin x+\cos 2x)+\frac{1}{2}=0\\ \\ \sin^2x+(1-2\sin^2x)^2-(\sin x+1-2\sin^2x)+\frac{1}{2}=0\\ \\ \sin^2x+1-4\sin^2x+4\sin^4x-\sin x-1+2\sin^2x+\frac{1}{2}=0\\ \\ 4\sin^4x-\sin^2x-\sin x+\frac{1}{2}=0\\ \\ 2\sin^2x(2\sin x-1)(2\sin x+1)-(2\sin x-1)=0\\ \\ (2\sin x-1)(4\sin^3x+2\sin^2x-1)=0](https://tex.z-dn.net/?f=%5Csin%5E2x%2B%5Ccos%5E22x-%28%5Csin+x%2B%5Ccos+2x%29%2B%5Cfrac%7B1%7D%7B2%7D%3D0%5C%5C+%5C%5C+%5Csin%5E2x%2B%281-2%5Csin%5E2x%29%5E2-%28%5Csin+x%2B1-2%5Csin%5E2x%29%2B%5Cfrac%7B1%7D%7B2%7D%3D0%5C%5C+%5C%5C+%5Csin%5E2x%2B1-4%5Csin%5E2x%2B4%5Csin%5E4x-%5Csin+x-1%2B2%5Csin%5E2x%2B%5Cfrac%7B1%7D%7B2%7D%3D0%5C%5C+%5C%5C+4%5Csin%5E4x-%5Csin%5E2x-%5Csin+x%2B%5Cfrac%7B1%7D%7B2%7D%3D0%5C%5C+%5C%5C+2%5Csin%5E2x%282%5Csin+x-1%29%282%5Csin+x%2B1%29-%282%5Csin+x-1%29%3D0%5C%5C+%5C%5C+%282%5Csin+x-1%29%284%5Csin%5E3x%2B2%5Csin%5E2x-1%29%3D0)
Произведение равно нулю, когда хотя бы один из множителей равно 0
![2\sin x-1=0~~~\Leftrightarrow~~~ \sin x=\frac{1}{2}~~~\Leftrightarrow~~~ x=(-1)^k\cdot\frac{\pi}{6}+\pi k,k \in \mathbb{Z}](https://tex.z-dn.net/?f=2%5Csin+x-1%3D0~~~%5CLeftrightarrow~~~+%5Csin+x%3D%5Cfrac%7B1%7D%7B2%7D~~~%5CLeftrightarrow~~~+x%3D%28-1%29%5Ek%5Ccdot%5Cfrac%7B%5Cpi%7D%7B6%7D%2B%5Cpi+k%2Ck+%5Cin+%5Cmathbb%7BZ%7D)
![4\sin^3x+2\sin^2x-1=0\\ \\ 4\sin^3x-2\sin^2x+4\sin^2x-2\sin x+2\sin x-1=0\\\\ 2\sin^2x(2\sin x-1)+2\sin x(2\sin x-1)+2\sin x-1=0\\ \\ (2\sin x-1)(2\sin^2x+2\sin x+1)=0\\ \\ 2\sin^2x+2\sin x+1=0](https://tex.z-dn.net/?f=4%5Csin%5E3x%2B2%5Csin%5E2x-1%3D0%5C%5C+%5C%5C+4%5Csin%5E3x-2%5Csin%5E2x%2B4%5Csin%5E2x-2%5Csin+x%2B2%5Csin+x-1%3D0%5C%5C%5C%5C+2%5Csin%5E2x%282%5Csin+x-1%29%2B2%5Csin+x%282%5Csin+x-1%29%2B2%5Csin+x-1%3D0%5C%5C+%5C%5C+%282%5Csin+x-1%29%282%5Csin%5E2x%2B2%5Csin+x%2B1%29%3D0%5C%5C+%5C%5C+2%5Csin%5E2x%2B2%5Csin+x%2B1%3D0)
Решаем как квадратное уравнение относительно sin x
![D=b^2-4ac=2^2-4\cdot2\cdot1=4-8=-4<0](https://tex.z-dn.net/?f=D%3Db%5E2-4ac%3D2%5E2-4%5Ccdot2%5Ccdot1%3D4-8%3D-4%3C0)
Это уравнение действительных корня не имеет.
Отбор корней на отрезке [7π/2; 7π]
k = 4; x = π/6 + 4π = 25π/6
k = 5; x = -π/6 + 5π = 29π/6
k = 6; x = π/6 + 6π = 37π/6
k = 7; x = -π/6 + 7π = 41π/6
Ответ:
1 если x -3,5 , то y=-22 , если y=-5 , то x=5
график функции не проходит через эту точку
(2,5;-4) (-7;4)
y=6 если x=3
дальше сам)))
Объяснение: