Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 743

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\[1)\ tg\ 2x \leq 1\]

\[- \frac{\pi}{2} + \pi n < 2x \leq arctg\ 1 + \pi n\]

\[- \frac{\pi}{2} + \pi n < 2x \leq \frac{\pi}{4} + \pi n\]

\[- \frac{\pi}{4} + \frac{\text{πn}}{2} < x \leq \frac{\pi}{8} + \frac{\text{πn}}{2}\]

\[\left( - \frac{\pi}{2};\ \pi \right):\]

\[- \frac{\pi}{2} < x_{1} \leq - \frac{3\pi}{8}\]

\[- \frac{\pi}{4} < x_{2} \leq \frac{\pi}{8}\]

\[\frac{\pi}{4} < x_{3} \leq \frac{5\pi}{8}\]

\[\frac{3\pi}{4} < x_{4} < \pi.\]

\[2)\ tg\ 3x < - \sqrt{3}\]

\[- \frac{\pi}{2} + \pi n < 3x < arctg\left( - \sqrt{3} \right) + \pi n\]

\[- \frac{\pi}{2} + \pi n < 3x < - arctg\ \sqrt{3} + \pi n\]

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

\[- \frac{\pi}{6} + \frac{\text{πn}}{3} < x < - \frac{\pi}{9} + \frac{\text{πn}}{3}\]

\[\left( - \frac{\pi}{2};\ \pi \right):\]

\[- \frac{\pi}{2} < x_{1} < - \frac{4\pi}{9}\]

\[- \frac{\pi}{6} < x_{2} < - \frac{\pi}{9}\]

\[\frac{\pi}{6} < x_{3} < \frac{2\pi}{9}\]

\[\frac{\pi}{2} < x_{4} < \frac{5\pi}{9}\]

\[\frac{5\pi}{6} < x_{5} < \frac{8\pi}{9}.\]