Question

упростите 8 соs10cos20cos40

Answer 1

$8cdot cos10cdot cos20cdot cos40= frac{4cdot (2cdot sin10cdot cos10)cdot cos20cdot cos40}{sin10} = \\=frac{2cdot (2cdot sin20cdot cos20)cdot cos40}{sin10} = frac{2cdot sin40cdot cos40}{sin10} = frac{sin80}{sin10} =\\= frac{sin(90-10)}{sin10} = frac{cos10}{sin10} =ctg10$