Question

помогите решить даю 100б​

Answer 1

Ответ:

Применяем формулы произведений тригонометрических функций  sin на cos ,  cos на cos .

$\displaystyle 8)\ \ cos\frac{\pi}{10}\cdot sin\frac{\pi}{5}=\frac{1}{2}\cdot \Big(sin(\frac{\pi}{10}+\frac{\pi}{5})+sin(\frac{\pi}{5}-\frac{\pi}{10})\, \Big)=\frac{1}{2}\cdot \Big(sin\frac{3\pi }{10}+sin\frac{\pi}{10}\Big)\\\\\\9)\ \ cos\frac{\pi}{5}\cdot cos\frac{\pi}{8}=\frac{1}{2}\cdot \Big(cos(\frac{\pi}{5}+\frac{\pi}{8})+cos(\frac{\pi}{5}-\frac{\pi}{8})\, \Big)=\frac{1}{2}\cdot \Big(cos\frac{13\pi }{40}+cos\frac{3\pi}{40}\Big)$

$\displaystyle 10)\ \ sin\frac{\pi}{10}\cdot cos\frac{\pi}{8}=\frac{1}{2}\cdot \Big(sin(\frac{\pi}{10}+\frac{\pi}{8})+sin(\frac{\pi}{10}-\frac{\pi}{8})\, \Big)=\frac{1}{2}\cdot \Big(sin\frac{9\pi }{40}+sin\frac{-\pi}{40}\Big)=\\\\\\=\frac{1}{2}\cdot \Big(sin\frac{9\pi }{40}-sin\frac{\pi}{40}\Big)$