Cos^2(2x)-2cos(2x) больше или равно 0
Применены : замена переменной, ограниченность косинуса, метод интервалов
![cos2x(cos2x-2) \geq 0 \ \ |:(cos2x-2) \\ cos2x \leq 0 \\ \\cos2x = 0 \\ 2x= \frac{ \pi }{2} + \pi n \ \Leftrightarrow \
\begin{bmatrix} \frac{\pi }{2}+2\pi n \\ \\ \frac{3\pi }{2}+2\pi n \end{matrix} \\ \\ \frac{\pi }{2}+2\pi n \leq 2x \leq \frac{3\pi }{2}+2\pi n \ \ |:2 \\ \\ \frac{\pi }{4}+\pi n \leq x \leq \frac{3\pi }{4}+\pi n \ \\ \\ OTBET: \ x \in [\frac{\pi }{4}+\pi n; \ \frac{3\pi }{4}+\pi n], \ n \in Z](https://tex.z-dn.net/?f=cos2x%28cos2x-2%29+%5Cgeq+0+%5C+%5C+%7C%3A%28cos2x-2%29+%5C%5C++cos2x+%5Cleq+0+%5C%5C++%5C%5Ccos2x+%3D+0+%5C%5C++2x%3D+%5Cfrac%7B+%5Cpi+%7D%7B2%7D+%2B+%5Cpi+n+%5C+%5CLeftrightarrow++%5C+%0A%5Cbegin%7Bbmatrix%7D+%5Cfrac%7B%5Cpi+%7D%7B2%7D%2B2%5Cpi+n+%5C%5C+%5C%5C++%5Cfrac%7B3%5Cpi+%7D%7B2%7D%2B2%5Cpi+n+%5Cend%7Bmatrix%7D+%5C%5C+%5C%5C+%5Cfrac%7B%5Cpi+%7D%7B2%7D%2B2%5Cpi+n+%5Cleq+2x+%5Cleq+%5Cfrac%7B3%5Cpi+%7D%7B2%7D%2B2%5Cpi+n+%5C+%5C+%7C%3A2+%5C%5C++%5C%5C+%5Cfrac%7B%5Cpi+%7D%7B4%7D%2B%5Cpi+n+%5Cleq+x+%5Cleq+%5Cfrac%7B3%5Cpi+%7D%7B4%7D%2B%5Cpi+n+%5C++%5C%5C++%5C%5C+OTBET%3A+%5C+x+%5Cin+%5B%5Cfrac%7B%5Cpi+%7D%7B4%7D%2B%5Cpi+n%3B+%5C+%5Cfrac%7B3%5Cpi+%7D%7B4%7D%2B%5Cpi+n%5D%2C+%5C+n+%5Cin+Z "cos2x(cos2x-2) \geq 0 \ \ |:(cos2x-2) \\ cos2x \leq 0 \\ \\cos2x = 0 \\ 2x= \frac{ \pi }{2} + \pi n \ \Leftrightarrow \
\begin{bmatrix} \frac{\pi }{2}+2\pi n \\ \\ \frac{3\pi }{2}+2\pi n \end{matrix} \\ \\ \frac{\pi }{2}+2\pi n \leq 2x \leq \frac{3\pi }{2}+2\pi n \ \ |:2 \\ \\ \frac{\pi }{4}+\pi n \leq x \leq \frac{3\pi }{4}+\pi n \ \\ \\ OTBET: \ x \in [\frac{\pi }{4}+\pi n; \ \frac{3\pi }{4}+\pi n], \ n \in Z")