Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 87

\[- \frac{\pi}{2} < x < \pi.\]

\[1)\ tg\ 2x = \sqrt{3}\]

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

\[x = \frac{\pi}{6} + \frac{\pi n}{2}.\]

\[Ответ:\ - \frac{\pi}{3};\ \frac{\pi}{6};\ \frac{2\pi}{3}.\]

\[2)\ tg\frac{x}{3} = - 1\]

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

\[x = - \frac{3\pi}{4} + 3\pi n.\]

\[Ответ:\ \ нет\ корней.\]

\[3)\ ctg\frac{x}{2} = - \frac{1}{\sqrt{3}}\]

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

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

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

\[Ответ:\ \ нет\ корней.\]

\[4)\ ctg\ 3x = 1\]

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

\[x = \frac{\pi}{12} + \frac{\pi n}{3}.\]

\[Ответ:\ - \frac{\pi}{4};\ \frac{\pi}{12};\ \frac{5\pi}{12};\ \frac{3\pi}{4}.\]