Question

Решить уравнение
√8sin(2x+П/6)+√6=0

Answer 1

Ответ:

$\sqrt{8} \sin(2x + \frac{\pi}{6} ) + \sqrt{6} = 0 \\ \sin(2x + \frac{\pi}{6} ) = - \sqrt{ \frac{6}{8} } \\ \sin(2x + \frac{\pi}{6} ) = - \frac{ \sqrt{3} }{2} \\ \\ 2x + \frac{\pi}{6} = - \frac{\pi}{6} + 2 \pi \: n \\ 2x = - \frac{\pi}{3} + 2\pi \: n \\ x_1 = - \frac{\pi}{6} + \pi \: n \\ \\ 2x + \frac{\pi}{6} = - \frac{5\pi}{6} + 2 \pi \: n \\ 2x = - \pi + 2\pi \: n \\ x_2 = - \frac{\pi}{2} + \pi \: n \\ \\ n\in \: Z$