a) sin - sin"; 5 10

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

В нашем случае $$x = \frac{\pi}{5}$$ и $$y = \frac{\pi}{10}$$.

$$sin(\frac{\pi}{5}) - sin(\frac{\pi}{10}) = 2cos(\frac{\frac{\pi}{5} + \frac{\pi}{10}}{2})sin(\frac{\frac{\pi}{5} - \frac{\pi}{10}}{2}) = 2cos(\frac{\frac{3\pi}{10}}{2})sin(\frac{\frac{\pi}{10}}{2}) = 2cos(\frac{3\pi}{20})sin(\frac{\pi}{20})$$.

Ответ: $$2cos(\frac{3\pi}{20})sin(\frac{\pi}{20})$$.