Question

помогите упростить : -2$\sqrt{3}$ cos(x + $\frac{7pi}{6}$)

Answer 1

$cos(\alpha +\beta )=cos\alpha *cos\beta -sin\alpha *sin\beta$$-2\sqrt{3}cos(x+\frac{7\pi }{6})=-2\sqrt{3}(cos(x)*cos(\frac{7\pi }{6} ) -sin(x)*sin(7\pi }{6} ))=\\ \\ =-2\sqrt{3}(cos(x)*(-\frac{\sqrt{3} }{2})-sin(x)*(-\frac{1}{2} ))=2\sqrt{3}* \frac{\sqrt{3} }{2}cos(x)-2\sqrt{3}*\frac{1}{2}sin(x)=\\ \\ =3cos(x)-\sqrt{3}sin(x)$