Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 578

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\[\cos{4x} = \frac{\sqrt{2}}{2}\]

\[4x = \pm \arccos\frac{\sqrt{2}}{2} + 2\pi n =\]

\[= \pm \frac{\pi}{4} + 2\pi n\]

\[x = \frac{1}{4} \bullet \left( \pm \frac{\pi}{4} + 2\pi n \right)\]

\[x = \pm \frac{\pi}{16} + \frac{\text{πn}}{2}.\]

\[|x| < \frac{\pi}{4}:\]

\[x_{1} = - \frac{\pi}{16}\text{\ \ }и\ \ x_{2} = \frac{\pi}{16}.\]