Question

Преобразуйте в произведение : 3-√ 3*ctg2a

Answer 1

$3-\sqrt3\cdot ctg2a=\sqrt3\cdot (\sqrt3-ctg2a)=\sqrt3\cdot (ctg\frac{\pi}{6}-ctg2a)=\\\\=\sqrt3\cdot \frac{sin(2a-\frac{\pi}{6})}{sin\frac{\pi}{6}\cdot sin32a}=\sqrt3\cdot \frac{sin(2a-\frac{\pi}{6})}{\frac{1}{2}\cdot sin2a}=2\sqrt3\cdot \frac{sin(2a-\frac{\pi}{6})}{sin2a} =\\\\=2\sqrt3\cdot sin(2a-\frac{\pi}{6})\cdot \frac{1}{sin2a}$