Question

Представьте в виде суммы sin(п/6+альфа)*sin альфа

Answer 1

$sin \alpha \cdot sin \beta =\frac{1}{2}\cdot \Big (cos( \alpha - \beta )-cos( \alpha + \beta )\Big )\\\\\\sin( \frac{\pi }{6} +\alpha )\cdot sin \alpha = \frac{1}{2} \cdot \Big (cos (\frac{\pi }{6}+ \alpha -\alpha )-cos(\frac{\pi}{6}+ \alpha + \alpha )\Big )=\\\\= \frac{1}{2}\cdot \Big (cos\frac{\pi}{6}-cos (\frac{\pi}{6} +2 \alpha )\Big )= \frac{1}{2}\cdot \Big ( \frac{\sqrt3}{2} -cos( \frac{\pi}{6}+2 \alpha )\Big )=\\\\=\frac{\sqrt3}{4}-\frac{1}{2}cos(\frac{\pi}{6}+2 \alpha )$