6) sin + sin"; 3 4'

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

В нашем случае $$x = \frac{\pi}{3}$$ и $$y = \frac{\pi}{4}$$.

$$sin(\frac{\pi}{3}) + sin(\frac{\pi}{4}) = 2sin(\frac{\frac{\pi}{3} + \frac{\pi}{4}}{2})cos(\frac{\frac{\pi}{3} - \frac{\pi}{4}}{2}) = 2sin(\frac{\frac{7\pi}{12}}{2})cos(\frac{\frac{\pi}{12}}{2}) = 2sin(\frac{7\pi}{24})cos(\frac{\pi}{24})$$.

Ответ: $$2sin(\frac{7\pi}{24})cos(\frac{\pi}{24})$$.