Уравнения, сводящиеся к простейшим заменой неизвестного. Задача 18

ОТВЕТ: \( \pm \dfrac{\pi }{6} + \pi k;\quad \,k \in Z.\)

\({\rm{ct}}{{\rm{g}}^2}x = 3\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{{\rm{ctg}}\,x = \sqrt 3 ,\,\,}\\{{\rm{ctg}}\,x = -\sqrt 3 }\end{array}\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = \dfrac{\pi }{6} + \pi k,\,\,\,\,}\\{x = -\dfrac{\pi }{6} + \pi k\,}\end{array}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,} \right.} \right.x =  \pm \dfrac{\pi }{6} + \pi k,\,\,\,\,\,\,\,\,k\, \in \,Z.\)

Ответ:  \( \pm \dfrac{\pi }{6} + \pi k;\quad \,k \in Z.\)