5. Используя формулы приведения: Вычислить: a) cos210°; б) cos315° + ctg150°; Упростить выражение: в) sin(2π-α)tg(π/2-α) / cos(π+α); *г) sin(23π/4) * tg(19π/6).

а) \( cos210° \) \( cos210° = cos(180° + 30°) = -cos30° = -\frac{\sqrt{3}}{2} \) б) \( cos315° + ctg150° \) \( cos315° = cos(360° - 45°) = cos45° = \frac{\sqrt{2}}{2} \) \( ctg150° = ctg(180° - 30°) = -ctg30° = -\sqrt{3} \) \( cos315° + ctg150° = \frac{\sqrt{2}}{2} - \sqrt{3} \) в) \( \frac{sin(2\pi - \alpha)tg(\frac{\pi}{2} - \alpha)}{cos(\pi + \alpha)} \) \( sin(2\pi - \alpha) = -sin\alpha \) \( tg(\frac{\pi}{2} - \alpha) = ctg\alpha \) \( cos(\pi + \alpha) = -cos\alpha \) \( \frac{-sin\alpha \cdot ctg\alpha}{-cos\alpha} = \frac{sin\alpha \cdot \frac{cos\alpha}{sin\alpha}}{cos\alpha} = \frac{cos\alpha}{cos\alpha} = 1 \) г) \( sin(\frac{23\pi}{4}) \cdot tg(\frac{19\pi}{6}) \) \( sin(\frac{23\pi}{4}) = sin(6\pi - \frac{\pi}{4}) = sin(-\frac{\pi}{4}) = -sin(\frac{\pi}{4}) = -\frac{\sqrt{2}}{2} \) \( tg(\frac{19\pi}{6}) = tg(3\pi + \frac{\pi}{6}) = tg(\pi + \frac{\pi}{6}) = tg(\frac{\pi}{6}) = \frac{\sqrt{3}}{3} \) \( sin(\frac{23\pi}{4}) \cdot tg(\frac{19\pi}{6}) = -\frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{3} = -\frac{\sqrt{6}}{6} \)