5 Вычислите: a) cos 315° + sin 210° + tg 420° б) sin 13π/6 - cos 11π/6 +ctg 11π/4

1. а) Вычисление \(\cos 315° + \sin 210° + \tan 420°\):
   • \(\cos 315° = \cos (360° - 45°) = \cos 45° = \frac{\sqrt{2}}{2}\)
   • \(\sin 210° = \sin (180° + 30°) = -\sin 30° = -\frac{1}{2}\)
   • \(\tan 420° = \tan (360° + 60°) = \tan 60° = \sqrt{3}\)
   • Сумма: \(\frac{\sqrt{2}}{2} - \frac{1}{2} + \sqrt{3}\)
2. б) Вычисление \(\sin \frac{13\pi}{6} - \cos \frac{11\pi}{6} + \cot \frac{11\pi}{4}\):
   • \(\sin \frac{13\pi}{6} = \sin (2\pi + \frac{\pi}{6}) = \sin \frac{\pi}{6} = \frac{1}{2}\)
   • \(\cos \frac{11\pi}{6} = \cos (2\pi - \frac{\pi}{6}) = \cos \frac{\pi}{6} = \frac{\sqrt{3}}{2}\)
   • \(\cot \frac{11\pi}{4} = \cot (2\pi + \frac{3\pi}{4}) = \cot \frac{3\pi}{4} = -1\)
   • Разность: \(\frac{1}{2} - \frac{\sqrt{3}}{2} - 1\)

Ответ: a) \(\frac{\sqrt{2}}{2} - \frac{1}{2} + \sqrt{3}\); б) \(\frac{1}{2} - \frac{\sqrt{3}}{2} - 1\)