Question

докажите справедливость равенства: cosп/7cos2п/7cos4п/7=-1/8

Answer 1

$cosfrac{pi}{7}cosfrac{2pi}{7}cosfrac{4pi}{7}=$

умножим и поделим на $8sinfrac{pi}{7}$

$cosfrac{pi}{7}*cosfrac{2pi}{7}*cosfrac{4pi}{7}=frac{8sinfrac{pi}{7}*cosfrac{pi}{7}*cosfrac{2pi}{7}*cosfrac{4pi}{7}}{8sinfrac{pi}{7}}=\ =frac{4sinfrac{2pi}{7}*cosfrac{2pi}{7}*cosfrac{4pi}{7}}{8sinfrac{pi}{7}}=frac{2sinfrac{4pi}{7}*cosfrac{4pi}{7}}{8sinfrac{pi}{7}}=frac{sinfrac{8pi}{7}}{8sinfrac{pi}{7}}=-frac{sinfrac{pi}{7}}{8sinfrac{pi}{7}}=-frac{1}{8}$