Question

(cosx-1)*(2cosx-√3)=0

решить тригонометрическое уравнение

Answer 1

$(\cos x-1)(2\cos x-\sqrt{3} )=0$

$\left[\begin{array}{l} \cos x-1=0\\ 2\cos x-\sqrt{3} =0 \end{array}$

$\left[\begin{array}{l} \cos x=1\\ \cos x=\dfrac{\sqrt{3} }{2} \end{array}$

$\left[\begin{array}{l} x=2\pi n,\ n\in\mathbb{Z}\\ x=\pm \dfrac{\pi}{6}+2\pi n ,\ n\in\mathbb{Z} \end{array}$

Ответ: $2\pi n;\ \pm \dfrac{\pi}{6}+2\pi n ,\ n\in\mathbb{Z} \end{array}$