Sinn/2+cosx/3-tg(-\nπ/6) 20√3cos(-)sin(-). 16√3sin(60°). 36√3tg(210°). 12v2cos(-45°). 2√3tg sin π π 3 π sin--cos-+2tg 6 3 π - 4 cos 135 sin 210"+ctg300-tg316

Решение:

1. $$sin\frac{\pi}{2} + cos\frac{\pi}{3} - tg(-\frac{\pi}{6}) = 1 + \frac{1}{2} - (-\frac{\sqrt{3}}{3}) = 1 + \frac{1}{2} + \frac{\sqrt{3}}{3} = \frac{3}{2} + \frac{\sqrt{3}}{3} = \frac{9 + 2\sqrt{3}}{6}$$
2. $$20\sqrt{3}cos(-\frac{\pi}{3})sin(-\frac{\pi}{3}) = 20\sqrt{3} \cdot \frac{1}{2} \cdot (-\frac{\sqrt{3}}{2}) = -20\sqrt{3} \cdot \frac{\sqrt{3}}{4} = -\frac{20 \cdot 3}{4} = -15$$
3. $$16\sqrt{3}sin(60°) = 16\sqrt{3} \cdot \frac{\sqrt{3}}{2} = 16 \cdot \frac{3}{2} = 8 \cdot 3 = 24$$
4. $$36\sqrt{3}tg(210°) = 36\sqrt{3} \cdot tg(180° + 30°) = 36\sqrt{3} \cdot tg(30°) = 36\sqrt{3} \cdot \frac{\sqrt{3}}{3} = 36 \cdot \frac{3}{3} = 36$$
5. $$12\sqrt{2}cos(-45°) = 12\sqrt{2} \cdot cos(45°) = 12\sqrt{2} \cdot \frac{\sqrt{2}}{2} = 12 \cdot \frac{2}{2} = 12$$
6. $$2\sqrt{3}tg\frac{\pi}{3}sin\frac{\pi}{6} = 2\sqrt{3} \cdot \sqrt{3} \cdot \frac{1}{2} = 2 \cdot 3 \cdot \frac{1}{2} = 3$$
7. $$sin\frac{\pi}{6} - cos\frac{\pi}{3} + 2tg\frac{\pi}{4} = \frac{1}{2} - \frac{1}{2} + 2 \cdot 1 = 2$$
8. $$cos135° \cdot sin210° + ctg300° \cdot tg315° = cos(180°-45°) \cdot sin(180°+30°) + ctg(360°-60°) \cdot tg(360°-45°) = -cos45° \cdot (-sin30°) + (-ctg60°) \cdot (-tg45°) = -\frac{\sqrt{2}}{2} \cdot (-\frac{1}{2}) + (-\frac{\sqrt{3}}{3}) \cdot (-1) = \frac{\sqrt{2}}{4} + \frac{\sqrt{3}}{3} = \frac{3\sqrt{2} + 4\sqrt{3}}{12}$$

Ответ: смотри решение выше