Question

Преобразуйте в произведение cos3пи/11+ cos5пи/11+cos7пи/11

Answer 1

$cos\frac{3\pi}{11}+cos\frac{5\pi}{11}+cos\frac{7\pi}{11}=cos\frac{5\pi}{11}+2cos\frac{\frac{3\pi}{11}+\frac{7\pi}{11}}{2}\cdot cos\frac{\frac{7\pi }{11}-\frac{3\pi}{11}}{2}=\\\\=cos\frac{5\pi}{11}+2cos\frac{5\pi}{11}\cdot cos\frac{2\pi }{11}=cos\frac{5\pi}{11}\cdot (1+2cos\frac{2\pi}{11})$