Question

Тригонометрия 9 класс

Answer 1

формула 

$cos(\alpha)-cos(\beta)=2*sin(\frac{\alpha+\beta}{2})*sin(\frac{\beta-\alpha}{2})$

$cos(\frac{\pi}{6}+a)-cos(\frac{\pi}{6}-a)=\\\\ =2*sin(\frac{[\frac{\pi}{6}+a]+[\frac{\pi}{6}-a]}{2})*sin(\frac{[\frac{\pi}{6}-a]-[\frac{\pi}{6}+a]}{2})=\\\\ =2*sin(\frac{\pi}{6})*sin(-a)=2*\frac{1}{2}*[-sin(a)]=-sin(a)=-\frac{\sqrt{3}}{4}$