ГДЗ по алгебре и начала математического анализа 10 класс Алимов Задание 574

\[\boxed{\mathbf{574}\mathbf{.}}\]

\[1)\cos x \bullet \cos{3x} = \sin{3x} \bullet \sin x\]

\[\cos x \bullet \cos{3x} - \sin{3x} \bullet \sin x = 0\]

\[\cos(x + 3x) = 0\]

\[\cos{4x} = 0\]

\[4x = \arccos 0 + \pi n = \frac{\pi}{2} + \pi n\]

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

\[x = \frac{\pi}{8} + \frac{\text{πn}}{4}\]

\[Ответ:\ \ \frac{\pi}{8} + \frac{\text{πn}}{4}.\]

\[2)\cos{2x} \bullet \cos x + \sin{2x} \bullet \sin x =\]

\[= 0\]

\[\cos(2x - x) = 0\]

\[\cos x = 0\]

\[x = \arccos 0 + \pi n\]

\[x = \frac{\pi}{2} + \pi n\]

\[Ответ:\ \ \frac{\pi}{2} + \pi n.\]