Question

Докажите равенство
$cos75*cos15= frac{1}{4}$

Answer 1

$cos75*cos15= frac{1}{4}\\cos(90-15)*cos15= frac{1}{4}\\sin15*cos15= frac{1}{4}\\ frac{1}{2}(2sin15*cos15)= frac{1}{4}\\ frac{1}{2}sin(2*15)= frac{1}{4}\\ frac{1}{2}sin30= frac{1}{4}\\ frac{1}{2}* frac{1}{2}= frac{1}{4}\\ frac{1}{4}= frac{1}{4}$