Question

4(cos(pi/5)-cos(2pi/5)) помогите пожалуйста

Answer 1

$4\cdot (cos\frac{\pi }{5}-cos\frac{2\pi }{5})=4\cdot 2\cdot sin\frac{3\pi }{5}\cdot sin\frac{\pi}{5}=8\cdot sin(\frac{\pi }{2}+\frac{\pi }{10})\cdot sin\frac{\pi }{5}=\\\\=\underline {8\cdot cos\frac{\pi}{10}\cdot sin\frac{\pi}{5}}=8\cdot cos\frac{\pi }{10}\cdot 2\, sin\frac{\pi }{10}\, cos \frac{\pi }{10}=\underline {16\cdot sin\frac{\pi }{10}\cdot cos^2\frac{\pi }{10}}$