29) (2 - 2 sin 300°)(2 - 2 cos 330°); 30) cos(-2π/3) + sin(5π/4)

Решение:

1. \( (2 - 2 \sin(300^{\circ}))(2 - 2 \cos(330^{\circ})) = (2 - 2(-\frac{\sqrt{3}}{2}))(2 - 2(\frac{\sqrt{3}}{2})) = (2 + \sqrt{3})(2 - \sqrt{3}) = 2^2 - (\sqrt{3})^2 = 4 - 3 = 1 \)
2. \( \cos(-\frac{2\pi}{3}) + \sin(\frac{5\pi}{4}) = \cos(\frac{2\pi}{3}) + \sin(\pi + \frac{\pi}{4}) = -\frac{1}{2} + (-\sin(\frac{\pi}{4})) = -\frac{1}{2} - \frac{\sqrt{2}}{2} = -\frac{1 + \sqrt{2}}{2} \)

Ответ: 29) 1; 30) -(1+√2)/2.