ππ. a) cos-cos 10 20

a) Используем формулу разности косинусов:$$cos(x) - cos(y) = -2sin(\frac{x+y}{2})sin(\frac{x-y}{2})$$

В нашем случае $$x = \frac{\pi}{10}$$ и $$y = \frac{\pi}{20}$$.

$$cos(\frac{\pi}{10}) - cos(\frac{\pi}{20}) = -2sin(\frac{\frac{\pi}{10} + \frac{\pi}{20}}{2})sin(\frac{\frac{\pi}{10} - \frac{\pi}{20}}{2}) = -2sin(\frac{\frac{3\pi}{20}}{2})sin(\frac{\frac{\pi}{20}}{2}) = -2sin(\frac{3\pi}{40})sin(\frac{\pi}{40})$$.

Ответ: $$-2sin(\frac{3\pi}{40})sin(\frac{\pi}{40})$$.