Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 100

\[1)\ arctg\ \frac{1 - x}{4} = \frac{\pi}{3}\]

\[\frac{1 - x}{4} = \sqrt{3}\]

\[1 - x = 4\sqrt{3}\]

\[x = 1 - 4\sqrt{3}.\]

\[Ответ:\ \ 1 - 4\sqrt{3}.\]

\[2)\ arctg\frac{1 + 2x}{3} = \frac{\pi}{4}\]

\[\frac{1 + 2x}{3} = 1\]

\[1 + 2x = 3\]

\[2x = 2\]

\[x = 1.\]

\[Ответ:\ \ 1.\]

\[3)\ arctg(2x + 1) = - \frac{\pi}{3}\]

\[2x + 1 = - \sqrt{3}\]

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

\[x = - \frac{1 + \sqrt{3}}{2}.\]

\[Ответ:\ - \frac{1 + \sqrt{3}}{2}.\]

\[4)\ arctg(2 - 3x) = - \frac{\pi}{4}\]

\[2 - 3x = - 1\]

\[3x = 3\]

\[x = 1.\]

\[Ответ:\ \ 1.\]