Найти значение выражения: 1) cos 135°; 2) sin 8π; 3 3) tg 7π; 3 4) cos²π - sin2π . 8 8

Ответ: 1) -√2/2; 2) 0; 3) -√3; 4) 1/2

1. cos 135° = cos (180° - 45°) = -cos 45° = -\(\frac{\sqrt{2}}{2}\)
2. sin \(\frac{8\pi}{3}\) = sin (2\(\pi\) + \(\frac{2\pi}{3}\)) = sin \(\frac{2\pi}{3}\) = sin (\(\pi\) - \(\frac{\pi}{3}\)) = sin \(\frac{\pi}{3}\) = \(\frac{\sqrt{3}}{2}\)
3. tg \(\frac{7\pi}{3}\) = tg (2\(\pi\) + \(\frac{\pi}{3}\)) = tg \(\frac{\pi}{3}\) = \(\sqrt{3}\)
4. cos²\(\frac{\pi}{8}\) - sin²\(\frac{\pi}{8}\) = cos (2 \(\cdot\) \(\frac{\pi}{8}\)) = cos \(\frac{\pi}{4}\) = \(\frac{\sqrt{2}}{2}\)

Ответ: 1) -√2/2; 2) \(\frac{\sqrt{3}}{2}\); 3) \(\sqrt{3}\); 4) \(\frac{\sqrt{2}}{2}\)