Question

решите уравнение tg (x - п/6) = -√3

Answer 1

$tgleft(x-fracpi6right)=-sqrt3\\frac{tgx-tgfracpi6}{1+tgxtgfracpi6}=-sqrt3\frac{tgx-frac1{sqrt3}}{1+frac{tgx}{sqrt3}}=-sqrt3\tgx-frac1{sqrt3}=-sqrt3-tgx\tgx+tgx=frac1{sqrt3}-sqrt3\2tgx=frac{1-3}{sqrt3}=-frac{2}{sqrt3}\tgx=-frac1{sqrt3}\x=frac{5pi}6+pi n,;ninmathbb{Z}$