y(-x)=1-cos(-x)/1+cos(-x)=1-cosx/1+cosx=y(x) четная
y(-x)=cos(-x-pi/2)-(-x)^2=cos(x+pi/2)-x^2=-cos(x-pi/2)-x^2
sqrt(1-2sinx)
-1<=sinx<=1
-2<=2sin2x<=2
3>=1-2sinx>=-1
[-1;3]
![log _{3} ^{2}x-2log _{3}x=3\\\\log _{3} ^{2} x -2log _{3}x-3=0](https://tex.z-dn.net/?f=log+_%7B3%7D+%5E%7B2%7Dx-2log+_%7B3%7Dx%3D3%5C%5C%5C%5Clog+_%7B3%7D+%5E%7B2%7D+x+-2log+_%7B3%7Dx-3%3D0++)
ОДЗ: x > 0
Сделаем замену
![log _{3}x=m](https://tex.z-dn.net/?f=log+_%7B3%7Dx%3Dm+)
m² - 2m - 3 = 0
D = (- 2)² - 4 * 1 * ( - 3) = 4 + 12 = 16 = 4²
![m _{1} = \frac{2+4}{2}=3\\\\m _{2}= \frac{2-4}{2}=-1\\\\log _{3}x _{1} =3\\\\x _{1} =3 ^{3}=27\\\\log _{3}x _{2} =-1\\\\x _{2}=3 ^{-1}= \frac{1}{3}](https://tex.z-dn.net/?f=m+_%7B1%7D+%3D+%5Cfrac%7B2%2B4%7D%7B2%7D%3D3%5C%5C%5C%5Cm+_%7B2%7D%3D+%5Cfrac%7B2-4%7D%7B2%7D%3D-1%5C%5C%5C%5Clog+_%7B3%7Dx+_%7B1%7D++%3D3%5C%5C%5C%5Cx+_%7B1%7D+%3D3+%5E%7B3%7D%3D27%5C%5C%5C%5Clog+_%7B3%7Dx+_%7B2%7D+%3D-1%5C%5C%5C%5Cx+_%7B2%7D%3D3+%5E%7B-1%7D%3D+%5Cfrac%7B1%7D%7B3%7D++++++++)
ОДЗ: x > 0
![lg(x+1,5) = - lgx\\\\lg(x+1,5)+lgx=0\\\\lgx(x+1,5)=0\\\\x(x+1,5)=10 ^{0}\\\\x(x+1,5) = 1](https://tex.z-dn.net/?f=lg%28x%2B1%2C5%29+%3D+-+lgx%5C%5C%5C%5Clg%28x%2B1%2C5%29%2Blgx%3D0%5C%5C%5C%5Clgx%28x%2B1%2C5%29%3D0%5C%5C%5C%5Cx%28x%2B1%2C5%29%3D10+%5E%7B0%7D%5C%5C%5C%5Cx%28x%2B1%2C5%29+%3D+1+)
x² + 1,5x - 1 = 0
D = 1,5² - 4 * 1 * ( -1) = 2,25 + 4 = 6,25 = 2,5²
![X _{1}= \frac{-1,5+2,5}{2}= \frac{1}{2}\\\\X _{2} = \frac{-1,5-2,5}{2}= \frac{-4}{2}=-2](https://tex.z-dn.net/?f=X+_%7B1%7D%3D+%5Cfrac%7B-1%2C5%2B2%2C5%7D%7B2%7D%3D+%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5CX+_%7B2%7D+%3D+%5Cfrac%7B-1%2C5-2%2C5%7D%7B2%7D%3D+%5Cfrac%7B-4%7D%7B2%7D%3D-2+++++)
x = - 2 - не подходит
Ответ: 0,5