π. r) sin-sin 3 11

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

В нашем случае $$x = \frac{\pi}{3}$$ и $$y = \frac{\pi}{11}$$.

$$sin(\frac{\pi}{3}) - sin(\frac{\pi}{11}) = 2cos(\frac{\frac{\pi}{3} + \frac{\pi}{11}}{2})sin(\frac{\frac{\pi}{3} - \frac{\pi}{11}}{2}) = 2cos(\frac{\frac{14\pi}{33}}{2})sin(\frac{\frac{8\pi}{33}}{2}) = 2cos(\frac{7\pi}{33})sin(\frac{4\pi}{33})$$.

Ответ: $$2cos(\frac{7\pi}{33})sin(\frac{4\pi}{33})$$.