Question

решите пожалуйста
  cos20cos40cos80=

Answer 1

$cos20cos40cos80=frac{1}{2sin20}cdot (2sin20cos20)cos40cos80=\\=frac{1}{2sin20}cdot sin40cos40cos80=frac{1}{4sin20}cdot (2sin40cos40)cos80=\\=frac{1}{4sin20}cdot sin80cos80=frac{1}{8sin20}cdot 2sin80cos80=frac{sin160}{8sin20}=\\=frac{sin(180-20)}{8sin20}=frac{sin20}{8sin20}=frac{1}{8}$