Question

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

Answer 1

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