Решебник по алгебре и начала математического анализа 10 класс Алимов Задание 614

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\[1)\ arctg\ (5x - 1) = \frac{\pi}{4}\]

\[\text{arctg\ }(5x - 1) = arctg\ 1\]

\[5x - 1 = 1\]

\[5x = 2\]

\[x = \frac{2}{5}\]

\[x = 0,4\]

\[Ответ:\ \ x = 0,4\]

\[2)\ arctg\ (3 - 5x) = - \frac{\pi}{3}\]

\[\text{arctg\ }(3 - 5x) = arctg\ \left( - \sqrt{3} \right)\]

\[\text{arctg\ }(3 - 5x) = - arctg\ \left( \sqrt{3} \right)\]

\[3 - 5x = - \sqrt{3}\]

\[5x = 3 + \sqrt{3}\]

\[x = \frac{3 + \sqrt{3}}{5}\]

\[Ответ:\ \ x = \frac{3 + \sqrt{3}}{5}.\]