17.4. a) arcctg (-1) + arctg (-1); б) arcsin (-√2/2) + arcctg (-√3); в) arcctg (-√3/3) - arctg √3/3; г) arccos (-1/2) - arcctg (-√3).

Решение:

• a) \( \operatorname{arcctg} (-1) + \operatorname{arctg} (-1) = 135^{\circ} + (-45^{\circ}) = 90^{\circ} = \frac{\pi}{2} \)
• б) \( \arcsin \left(-\frac{\sqrt{2}}{2}\right) + \operatorname{arcctg} (-\sqrt{3}) = -45^{\circ} + 150^{\circ} = 105^{\circ} = \frac{7\pi}{12} \)
• в) \( \operatorname{arcctg} \left(-\frac{\sqrt{3}}{3}\right) - \operatorname{arctg} \frac{\sqrt{3}}{3} = 120^{\circ} - 30^{\circ} = 90^{\circ} = \frac{\pi}{2} \)
• г) \( \arccos \left(-\frac{1}{2}\right) - \operatorname{arcctg} (-\sqrt{3}) = 120^{\circ} - 150^{\circ} = -30^{\circ} = -\frac{\pi}{6} \)

Ответ: а) \( \frac{\pi}{2} \); б) \( \frac{7\pi}{12} \); в) \( \frac{\pi}{2} \); г) \( -\frac{\pi}{6} \).