1. Вычислите: 1) a) 3 cos 60°-2 sin 30°+6 ctg 60°-2 ctg 30°; 6) sin(-30°)+cos(-60°)-2 tg(-30°) ctg (-60°); B) 5 sin (-45°)+5 cos(-45°)-3 tg (-30°)+sin(-30°); 2) a) 3 cos-2 sin+3tg-ctg 6) sin (-x)+2cos(-)-3 sin+3 cos(-); B) 6tg(-)ctg(-)+sin(-)-5 cos (-π).

1) a) 3 cos 60°-2 sin 30°+6 ctg 60°-2 ctg 30° =

\[ = 3 \cdot \frac{1}{2} - 2 \cdot \frac{1}{2} + 6 \cdot \frac{\sqrt{3}}{3} - 2 \cdot \sqrt{3} = \frac{3}{2} - 1 + 2\sqrt{3} - 2\sqrt{3} = \frac{1}{2} \]

Ответ: \(\frac{1}{2}\)

б) sin(-30°)+cos(-60°)-2 tg(-30°) ctg (-60°) =

\[ = -sin(30°) + cos(60°) - 2 \cdot (-tg(30°)) \cdot (-ctg(60°)) = -\frac{1}{2} + \frac{1}{2} - 2 \cdot \frac{\sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} = 0 - 2 \cdot \frac{1}{3} = -\frac{2}{3} \]

Ответ: \(-\frac{2}{3}\)

в) 5 sin (-45°)+5 cos(-45°)-\sqrt{3} tg (-30°)+sin(-30°) =

\[ = -5 sin(45°) + 5 cos(45°) - \sqrt{3} \cdot (-tg(30°)) - sin(30°) = -5 \cdot \frac{\sqrt{2}}{2} + 5 \cdot \frac{\sqrt{2}}{2} + \sqrt{3} \cdot \frac{\sqrt{3}}{3} - \frac{1}{2} = 0 + \frac{3}{3} - \frac{1}{2} = 1 - \frac{1}{2} = \frac{1}{2} \]

Ответ: \(\frac{1}{2}\)

2) a) 3 cos(\(\frac{\pi}{3}\))-2 sin(\(\frac{\pi}{6}\))+3tg(\(\frac{\pi}{4}\))-ctg(\(\frac{\pi}{4}\)) =

\[ = 3 \cdot \frac{1}{2} - 2 \cdot \frac{1}{2} + 3 \cdot 1 - 1 = \frac{3}{2} - 1 + 3 - 1 = \frac{3}{2} + 1 = \frac{5}{2} \]

Ответ: \(\frac{5}{2}\)

б) sin (-π)+2cos(-\(\frac{\pi}{2}\))-3 sin(\(\frac{3\pi}{2}\))+3 cos(-\(\frac{\pi}{4}\)) =

\[ = -sin(\pi) + 2 cos(-\frac{\pi}{2}) - 3 sin(\frac{3\pi}{2}) + 3 cos(-\frac{\pi}{4}) = 0 + 2 \cdot 0 - 3 \cdot (-1) + 3 \cdot \frac{\sqrt{2}}{2} = 0 + 0 + 3 + \frac{3\sqrt{2}}{2} = 3 + \frac{3\sqrt{2}}{2} \]

Ответ: \(3 + \frac{3\sqrt{2}}{2}\)

в) 6tg(-\(\frac{\pi}{3}\))ctg(-\(\frac{\pi}{6}\))+sin(-\(\frac{\pi}{2}\))-5 cos (-π) =

\[ = 6 \cdot (-tg(\frac{\pi}{3})) \cdot (-ctg(\frac{\pi}{6})) + sin(-\frac{\pi}{2}) - 5 cos(-\pi) = 6 \cdot (-\sqrt{3}) \cdot (-\sqrt{3}) - 1 - 5 \cdot (-1) = 6 \cdot 3 - 1 + 5 = 18 + 4 = 22 \]

Ответ: 22