Question

2tg(2x - pi/6) - 4 = 0

Answer 1

$2\,\mathrm{tg}\left(2x - \dfrac{\pi }{6} \right) - 4 = 0$

$2\,\mathrm{tg}\left(2x - \dfrac{\pi }{6} \right) = 4$

$\mathrm{tg}\left(2x - \dfrac{\pi }{6} \right) = 2$

$2x - \dfrac{\pi }{6} =\mathrm{arctg}\, 2+\pi n$

$2x = \dfrac{\pi }{6} +\mathrm{arctg}\, 2+\pi n$

$x = \dfrac{\pi }{12} +\dfrac{1}{2} \,\mathrm{arctg}\, 2+\dfrac{\pi n}{2} ,\ n\in\mathbb{Z}$

Ответ: $\dfrac{\pi }{12} +\dfrac{1}{2} \,\mathrm{arctg}\, 2+\dfrac{\pi n}{2} ,\ n\in\mathbb{Z}$