2 Найти значение выражения: 1) cos 135°; 2) sin 8π/3; 3) tg 7π/3; 4) cos² π/8 - sin² π/8

1) $$cos 135° = cos (180° - 45°) = -cos 45° = -\frac{\sqrt{2}}{2}$$

2) $$sin \frac{8\pi}{3} = sin \left(2\pi + \frac{2\pi}{3}\right) = sin \frac{2\pi}{3} = sin \left(\pi - \frac{\pi}{3}\right) = sin \frac{\pi}{3} = \frac{\sqrt{3}}{2}$$

3) $$tg \frac{7\pi}{3} = tg \left(2\pi + \frac{\pi}{3}\right) = tg \frac{\pi}{3} = \sqrt{3}$$

4) $$cos^2 \frac{\pi}{8} - sin^2 \frac{\pi}{8} = cos \left(2 \cdot \frac{\pi}{8}\right) = cos \frac{\pi}{4} = \frac{\sqrt{2}}{2}$$

Ответ:

1. $$cos 135° = -\frac{\sqrt{2}}{2}$$
2. $$sin \frac{8\pi}{3} = \frac{\sqrt{3}}{2}$$
3. $$tg \frac{7\pi}{3} = \sqrt{3}$$
4. $$cos^2 \frac{\pi}{8} - sin^2 \frac{\pi}{8} = \frac{\sqrt{2}}{2}$$