Question

Вычислите:cos 11П/56 cos 3П/56 - sin11П/42sin17П/42

Answer 1

$cos\frac{11\pi}{56}*cos\frac{3\pi}{56}-sin\frac{11\pi}{42}*sin\frac{17\pi}{42}\\\\ \frac{cos\frac{\pi}{7}+cos\frac{\pi}{4}}{2}-\frac{cos\frac{\pi}{7}-cos\frac{2\pi}{3}}{2}=\\\\ \frac{cos\frac{\pi}{7}+\frac{\sqrt{2}}{2}}{2}-\frac{cos\frac{\pi}{7}+\frac{1}{2}}{2}=\\\\ \frac{\sqrt{2}}{4}-\frac{1}{4}=\frac{\sqrt{2}-1}{4}$

Answer 2

Перед вами формула:
$cos(x+y)=> \\ cos( \frac{11 \pi }{56} - \frac{3 \pi }{42} )=cos( \frac{11 \pi }{56} - \frac{ \pi }{14} )=cos( \frac{11 \pi }{56} - \frac{4 \pi }{56} )=cos \frac{7 \pi }{56} =cos \frac{ \pi }{8}$