Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 598

\[\boxed{\mathbf{598}\mathbf{.}}\]

\[\sin\frac{x}{2} = \frac{\sqrt{3}}{2}\]

\[\frac{x}{2} = ( - 1)^{n} \bullet \arcsin\frac{\sqrt{3}}{2} + \pi n =\]

\[= ( - 1)^{n} \bullet \frac{\pi}{3} + \pi n\]

\[x = 2 \bullet \left( ( - 1)^{n} \bullet \frac{\pi}{3} + \pi n \right)\]

\[x = ( - 1)^{n} \bullet \frac{2\pi}{3} + 2\pi n.\]

\[\log_{\pi}(x - 4\pi) < 1:\]

\[\left\{ \begin{matrix} x - 4\pi < \pi \\ x - 4\pi > 0 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x < 5\pi \\ x > 4\pi \\ \end{matrix} \right.\ \ \ \ \Longrightarrow \ \]

\[\Longrightarrow 4\pi < x < 5\pi.\]

\[x_{1} = \frac{2\pi}{3} + 2 \bullet 2\pi\]

\[x = \frac{2\pi}{3} + 4\pi\]

\[x = \frac{14\pi}{3}.\]