Question

Тригонометрия. Плиииз

Answer 1

Решение на листочке...

Answer 2

$A= cos\frac{2\pi }{7}+cos\frac{4\pi }{7}+cos\frac{6\pi }{7}=[\; cos\frac{6\pi}{7}=cos(\pi -\frac{\pi}{7})=-cos\frac{\pi}{7}\; ]=\\\\=cos\frac{2\pi }{7}+cos\frac{4\pi }{7}-cos\frac{\pi }{7} =A\\\\2\, sin \frac{\pi}{7}\cdot A=2\, sin \frac{\pi}{7}\cdot cos\frac{2\pi}{7}+2\, sin \frac{\pi }{7}\cdot cos\frac{4\pi}{7}-2\, sin \frac{\pi}{7}\cdot cos\frac{\pi}{7}=\\\\=(sin\frac{3\pi}{7}-sin\frac{\pi}{7})+(sin\frac{5\pi }{7}-sin\frac{3\pi}{7})-sin\frac{2\pi}{7}=$

$=-sin\frac{\pi}{7}+(sin\frac{5\pi }{7}-sin\frac{2\pi}{7})=$

$=-sin \frac{\pi}{7} +2\, sin\frac{3\pi }{14}\cdot \underbrace {cos\frac{\pi}{2}}_{0}=-sin \frac{\pi}{7} \\\\2sin\frac{\pi}{7} \cdot A=-sin\frac{\pi}{7}\\\\A=-\frac{sin\frac{\pi}{7}}{2\, sin\frac{\pi}{7}} =-\frac{1}{2}$