Question

Срочно 15 баллов алгебра

Answer 1

$cos\frac{5\pi}{12}-cos\frac{3\pi}{12}=cos75^\circ -cos45^\circ =cos(45^\circ+30^\circ)-cos45^\circ =\\\\=cos45^\circ \cdot cos30^\circ -sin45^\circ \cdot sin30^\circ -\frac{\sqrt2}{2}=\frac{\sqrt2}{2}\cdot \frac{\sqrt3}{2}-\frac{\sqrt2}{2}\cdot \frac{1}{2}-\frac{\sqrt2}{2}=\\\\=\frac{\sqrt6-\sqrt2-2\sqrt2}{4}=\frac{\sqrt6-3\sqrt2}{4}=\frac{\sqrt6\, (1-\sqrt3)}{4}$