Решебник по алгебре и начала математического анализа 10 класс Алимов Задание 749

\[\boxed{\mathbf{749}\mathbf{.}}\]

\[1)\ tg^{2}x < 1\]

\[- 1 < tg\ x < 1;\]

\[tg\ x > - 1\]

\[\text{arctg}( - 1) + \pi n < x < \frac{\pi}{2} + \pi n\]

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

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

\[tg\ x < 1\]

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

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

\[Ответ:\ - \frac{\pi}{4} + \pi n < x < \frac{\pi}{4} + \pi n.\]

\[2)\ tg^{2}x \geq 3;\]

\[tg\ x \leq - \sqrt{3}\ или\ tg\ x \geq \sqrt{3}.\]

\[tg\ x \leq - \sqrt{3}\]

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

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

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

\[tg\ x \geq \sqrt{3}\]

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

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

\[Ответ:\ \]

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

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

\[3)\ ctg\ x \geq - 1\]

\[\pi n < x \leq arcctg( - 1) + \pi n\]

\[\pi n < x \leq - arcctg\ 1 + \pi n.\]

\[Ответ:\ \ \pi n < x \leq - \frac{\pi}{4} + \pi n.\]

\[4)\ ctg\ x > \sqrt{3}\]

\[\pi n < x \leq arcctg\ \sqrt{3} + \pi n.\]

\[Ответ:\ \ \pi n < x \leq \frac{\pi}{6} + \pi n.\]