Упростите 8 соs10cos20cos40

[latex]8\cdot cos10\cdot cos20\cdot cos40= \frac{4\cdot (2\cdot sin10\cdot cos10)\cdot cos20\cdot cos40}{sin10} = \\\\=\frac{2\cdot (2\cdot sin20\cdot cos20)\cdot cos40}{sin10} = \frac{2\cdot sin40\cdot cos40}{sin10} = \frac{sin80}{sin10} =\\\\= \frac{sin(90-10)}{sin10} = \frac{cos10}{sin10} =ctg10[/latex]