Question

Тригонометрешаааа (((

Answer 1

$\sin 2x+\sqrt{3}\sin x=0\\ 2\sin x\cos x+\sqrt{3}\sin x=0\\ \\ \sin x(2\cos x+\sqrt{3})=0\\ \\ \sin x=0~~~\Longrightarrow~~~ x=\pi k,k \in \mathbb{Z}\\ \\ 2\cos x+\sqrt{3}=0~~~\Rightarrow~~~ \cos x=-\dfrac{\sqrt{3}}{2}~~~\Longrightarrow~~~ x=\pm\dfrac{5\pi}{6}+2\pi n,n \in \mathbb{Z}$

Корни, удовлетворяющие [5π/2; 7π/2]: 3π; 17π/6; 19π/6.