Question

Преобразуйте в произведение : 3-√ 3*ctg2a

Answer 1

$3-sqrt3cdot ctg2a=sqrt3cdot (sqrt3-ctg2a)=sqrt3cdot (ctgfrac{pi}{6}-ctg2a)=\\=sqrt3cdot frac{sin(2a-frac{pi}{6})}{sinfrac{pi}{6}cdot sin32a}=sqrt3cdot frac{sin(2a-frac{pi}{6})}{frac{1}{2}cdot sin2a}=2sqrt3cdot frac{sin(2a-frac{pi}{6})}{sin2a} =\\=2sqrt3cdot sin(2a-frac{pi}{6})cdot frac{1}{sin2a}$