\[1)\ ctg\ x < 1\]
\[\frac{\pi}{4} + \pi n < x < \pi + \pi n.\]
\[2)\ tg\ x \geq \sqrt{3}\]
\[\frac{\pi}{3} + \pi n \leq x < \frac{\pi}{2} + \pi n.\]
\[3)\ tg\ x \leq - \frac{\sqrt{3}}{3}\]
\[- \frac{\pi}{2} + \pi n < x \leq - \frac{\pi}{6} + \pi n.\]
\[4)\ tg\ x > - 1\]
\[- \frac{\pi}{4} + \pi n < x < \frac{\pi}{2} + \pi n.\]