3π5π r) cos + cos 8 4

r) Используем формулу суммы косинусов:$$cos(x) + cos(y) = 2cos(\frac{x+y}{2})cos(\frac{x-y}{2})$$

В нашем случае $$x = \frac{3\pi}{8}$$ и $$y = \frac{5\pi}{4}$$.

$$cos(\frac{3\pi}{8}) + cos(\frac{5\pi}{4}) = 2cos(\frac{\frac{3\pi}{8} + \frac{5\pi}{4}}{2})cos(\frac{\frac{3\pi}{8} - \frac{5\pi}{4}}{2}) = 2cos(\frac{\frac{13\pi}{8}}{2})cos(\frac{\frac{-7\pi}{8}}{2}) = 2cos(\frac{13\pi}{16})cos(\frac{-7\pi}{16})$$.

Так как $$cos(-x) = cos(x)$$, то получаем:

$$2cos(\frac{13\pi}{16})cos(\frac{-7\pi}{16}) = 2cos(\frac{13\pi}{16})cos(\frac{7\pi}{16})$$.

Ответ: $$2cos(\frac{13\pi}{16})cos(\frac{7\pi}{16})$$.