Вычислите а) [latex]cos \frac{ \pi }{9} cos \frac{ 2\pi }{9} cos \frac{4 \pi }{9} [/latex] б) [latex]cos \frac{ \pi }{7} cos \frac{2 \pi }{7}cos \frac{4 \pi }{7} [/latex]

[latex]a)\; cos\frac{\pi}{9}cos\frac{2\pi}{9}cos\frac{4\pi}{9}=\frac{1}{2sin\frac{\pi}{9}}\cdot (2sin\frac{\pi}{9}cos\frac{\pi}{9})\cdot cos\frac{2\pi}{9}cos\frac{4\pi}{9}=\\\\=\frac{1}{2sin\frac{\pi}{9}}\cdot sin\frac{2\pi}{9}cos\frac{2\pi}{9}cos\frac{4\pi}{9}=\frac{1}{2sin\frac{\pi}{9}}\cdot \frac{1}{2}sin\frac{4\pi}{9}cos\frac{4\pi}{9}=\\\\=\frac{1}{4sin\frac{\pi}{9}}\cdot \frac{1}{2}sin\frac{8\pi}{9}=\frac{sin\frac{8\pi }{9}}{8sin\frac{\pi }{9}}=\frac{sin(\pi -\frac{\pi }{9})}{8sin\frac{\pi }{9}}=[/latex]   [latex]=\frac{sin\frac{\pi }{9}}{8sin\frac{\pi}{9}}=\frac{1}{8}\\\\b)\; cos\frac{\pi}{7}cos\frac{2\pi }{7}cos\frac{4\pi}{7}=\frac{2sin\frac{\pi}{7}cos\frac{\pi}{7}cos\frac{2\pi}{7}cos\frac{4\pi}{7}}{2sin\frac{\pi}{7}}=\frac{sin\frac{2\pi}{7}cos\frac{2\pi }{7}cos\frac{4\pi }{7}}{2sin\frac{\pi}{7}}=\\\\=\frac{sin\frac{4\pi}{7}cos\frac{4\pi}{7}}{4sin\frac{\pi}{7}}=\frac{sin\frac{8\pi }{7}}{8sin\frac{\pi}{7}}=\frac{sin(\pi +\frac{\pi }{7})}{8sin\frac{\pi}{7}}=\frac{-sin\frac{\pi}{7}}{8sin\frac{\pi}{7}}=-\frac{1}{8}[/latex]