Question

Решите пожалуйста уравнение​

Answer 1

$2cos(\frac{x}{2} - \frac{\pi }{6} ) = \sqrt{3}$ | : 2

$cos(\frac{x}{2} - \frac{\pi }{6} ) = \frac{\sqrt{3} }{2}$

$\left \{ {{\frac{x}{2} - \frac{\pi }{6} = \frac{\pi }{6} +2\pi n} \atop {\frac{x}{2} - \frac{\pi }{6} = - \frac{\pi }{6} +2\pi n}} \right.$

$\left \{ {{\frac{x}{2} = \frac{\pi }{6} + \frac{\pi }{6} +2\pi n} \atop {\frac{x}{2} = \frac{\pi }{6} - \frac{\pi }{6} +2\pi n}} \right.$

$\left \{ {{\frac{x}{2} = \frac{\pi }{3} +2\pi n} \atop {\frac{x}{2} = 2\pi n}} \right.$

$\left \{ {x} = \frac{2\pi }{3} +4\pi n} \atop {x} = 4\pi n}} \right.$

Ответ: 2