Y`=-2+1/2*cos(x/2)
y`(π)=2+1/2*cosπ/2=2+1/2*0=2
(5a+7b)²=25a²+70ab+49b²
(0.4-x)²=0.16-0.8x+x²=x²-0.8x+0.16
(-3-x)²=(-1*(3+x))²=(-1)²(3+x)²=(3+x)²=9+6x+x²=x²+6x+9
![\lg \sin(2x)=\lg \sin x](https://tex.z-dn.net/?f=%5Clg+%5Csin%282x%29%3D%5Clg+%5Csin+x)
ОДЗ: ![\sin (2x) > 0;~~~\sin x > 0](https://tex.z-dn.net/?f=%5Csin+%282x%29+%3E+0%3B~~~%5Csin+x+%3E+0)
![\lg \sin(2x)=\lg \sin x\\ \sin(2x)=\sin x;\\ 2\sin x\cos x-\sin x=0;\\ \sin x(2\cos x-1)=0](https://tex.z-dn.net/?f=%5Clg+%5Csin%282x%29%3D%5Clg+%5Csin+x%5C%5C+%5Csin%282x%29%3D%5Csin+x%3B%5C%5C+2%5Csin+x%5Ccos+x-%5Csin+x%3D0%3B%5C%5C+%5Csin+x%282%5Ccos+x-1%29%3D0)
1) sin x = 0 - не походит по ОДЗ
![2)~~~2\cos x - 1 = 0;~~~ \cos x = \frac12;\\\\~~~~~x_1=\dfrac{\pi}3+2 \pi n,~n\in Z\\\\~~~~~x_2=-\dfrac{\pi}3+2 \pi k,~k\in Z](https://tex.z-dn.net/?f=2%29~~~2%5Ccos+x+-+1+%3D+0%3B~~~+%5Ccos+x+%3D+%5Cfrac12%3B%5C%5C%5C%5C~~~~~x_1%3D%5Cdfrac%7B%5Cpi%7D3%2B2+%5Cpi+n%2C~n%5Cin+Z%5C%5C%5C%5C~~~~~x_2%3D-%5Cdfrac%7B%5Cpi%7D3%2B2+%5Cpi+k%2C~k%5Cin+Z)
Проверка корней по ОДЗ
![x_1=\dfrac{\pi}3+2 \pi n;~~\sin \dfrac{\pi}3=\dfrac{\sqrt3}2>0;~~\sin \dfrac{2\pi}3=\dfrac{\sqrt3}2>0;\\\\x_2=-\dfrac{\pi}3+2 \pi k;~~\sin \Big(-\dfrac{\pi}3\Big)=-\dfrac{\sqrt3}2<0](https://tex.z-dn.net/?f=x_1%3D%5Cdfrac%7B%5Cpi%7D3%2B2+%5Cpi+n%3B~~%5Csin+%5Cdfrac%7B%5Cpi%7D3%3D%5Cdfrac%7B%5Csqrt3%7D2%3E0%3B~~%5Csin+%5Cdfrac%7B2%5Cpi%7D3%3D%5Cdfrac%7B%5Csqrt3%7D2%3E0%3B%5C%5C%5C%5Cx_2%3D-%5Cdfrac%7B%5Cpi%7D3%2B2+%5Cpi+k%3B~~%5Csin+%5CBig%28-%5Cdfrac%7B%5Cpi%7D3%5CBig%29%3D-%5Cdfrac%7B%5Csqrt3%7D2%3C0)
x₂ не подходит по ОДЗ.
Ответ: ![\boldsymbol{\dfrac{\pi}3+2 \pi n,~n\in Z}](https://tex.z-dn.net/?f=%5Cboldsymbol%7B%5Cdfrac%7B%5Cpi%7D3%2B2+%5Cpi+n%2C~n%5Cin+Z%7D)
Ответ:
Объяснение:
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