Question

ctg(4x+п/6) =корень3

Answer 1

$ctg\left (4x+\dfrac{\pi}{6}\right ) = \sqrt{3}\\\\\\4x + \dfrac{\pi}{6} = arcctg\sqrt{3} + \pi k\\\\\\4x + \dfrac{\pi}{6} = \dfrac{\pi}{6} + \pi k\\\\\\4x = \dfrac{\pi}{6} + \pi k - \dfrac{\pi}{6}\\\\\\4x = \pi k\\\\\\\boxed{x = \dfrac{\pi k}{4}}\ ,\ k\in\mathbb{Z}$

Answer 2

Ответ:

пk/4, k принадлежит Z

Пошаговое объяснение:

4x+ П/6 =arcctg (корень 3)

4x+ П/6 = П/6

4x+ П/6 = П/6 + пk

4x= пk

x= пk/4