Question

Решите уравнение tg (x - п/6) = -√3

Answer 1

$tg\left(x-\frac\pi6\right)=-\sqrt3\\\\\frac{tgx-tg\frac\pi6}{1+tgxtg\frac\pi6}=-\sqrt3\\\frac{tgx-\frac1{\sqrt3}}{1+\frac{tgx}{\sqrt3}}=-\sqrt3\\tgx-\frac1{\sqrt3}=-\sqrt3-tgx\\tgx+tgx=\frac1{\sqrt3}-\sqrt3\\2tgx=\frac{1-3}{\sqrt3}=-\frac{2}{\sqrt3}\\tgx=-\frac1{\sqrt3}\\x=\frac{5\pi}6+\pi n,\;n\in\mathbb{Z}$