Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 755

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

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

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

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

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

\[Ответ:\ \ x = 1 - 4\sqrt{3}.\]

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

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

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

\[1 + 2x = 3\]

\[2x = 2\]

\[x = 1.\]

\[Ответ:\ \ x = 1.\]

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

\[\text{arctg}(2x + 1) = - arctg\ \sqrt{3}\]

\[\text{arctg}(2x + 1) = arctg\left( - \sqrt{3} \right)\]

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

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

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

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

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

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

\[\text{arctg}(2 - 3x) = arctg( - 1)\]

\[2 - 3x = - 1\]

\[3x = 2 + 1\]

\[3x = 3\]

\[x = 1.\]

\[Ответ:\ \ x = 1.\]