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

Вычислим значения выражений: 1. cos 135° \( \cos(135^\circ) = \cos(180^\circ - 45^\circ) = -\cos(45^\circ) = -\frac{\sqrt{2}}{2} \) 2. sin(8π/3) \( \sin(\frac{8\pi}{3}) = \sin(\frac{6\pi}{3} + \frac{2\pi}{3}) = \sin(2\pi + \frac{2\pi}{3}) = \sin(\frac{2\pi}{3}) = \sin(120^\circ) = \sin(180^\circ - 60^\circ) = \sin(60^\circ) = \frac{\sqrt{3}}{2} \) 3. tg(7π/3) \( \tan(\frac{7\pi}{3}) = \tan(\frac{6\pi}{3} + \frac{\pi}{3}) = \tan(2\pi + \frac{\pi}{3}) = \tan(\frac{\pi}{3}) = \tan(60^\circ) = \sqrt{3} \) 4. cos²(π/8) - sin²(π/8) Используем формулу двойного угла: \( \cos^2(x) - \sin^2(x) = \cos(2x) \) \( \cos^2(\frac{\pi}{8}) - \sin^2(\frac{\pi}{8}) = \cos(2 \cdot \frac{\pi}{8}) = \cos(\frac{\pi}{4}) = \cos(45^\circ) = \frac{\sqrt{2}}{2} \)

Ответ: 1) -√2/2; 2) √3/2; 3) √3; 4) √2/2

1) cos 135° \[ \cos(135^\circ) = \cos(180^\circ - 45^\circ) = -\cos(45^\circ) = -\frac{\sqrt{2}}{2} \] 2) sin(8π/3) \[ \sin(\frac{8\pi}{3}) = \sin(\frac{6\pi}{3} + \frac{2\pi}{3}) = \sin(2\pi + \frac{2\pi}{3}) = \sin(\frac{2\pi}{3}) = \sin(120^\circ) = \sin(180^\circ - 60^\circ) = \sin(60^\circ) = \frac{\sqrt{3}}{2} \] 3) tg(7π/3) \[ \tan(\frac{7\pi}{3}) = \tan(\frac{6\pi}{3} + \frac{\pi}{3}) = \tan(2\pi + \frac{\pi}{3}) = \tan(\frac{\pi}{3}) = \tan(60^\circ) = \sqrt{3} \] 4) cos²(π/8) - sin²(π/8) Используем формулу двойного угла: \( \cos^2(x) - \sin^2(x) = \cos(2x) \) \[ \cos^2(\frac{\pi}{8}) - \sin^2(\frac{\pi}{8}) = \cos(2 \cdot \frac{\pi}{8}) = \cos(\frac{\pi}{4}) = \cos(45^\circ) = \frac{\sqrt{2}}{2} \]

Ответ: 1) -√2/2; 2) √3/2; 3) √3; 4) √2/2