Уравнения, сводящиеся к простейшим заменой неизвестного. Задача 16

ОТВЕТ: \(\dfrac{\pi }{4} + \dfrac{{\pi k}}{2};\quad k \in Z.\)

\({\rm{ct}}{{\rm{g}}^2}x = 1\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{{\rm{ctg}}\,x = 1,\,\,\,}\\{{\rm{ctg}}\,x = -1}\end{array}} \right.\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = \dfrac{\pi }{4} + \pi k,\,\,\,\,}\\{x = -\dfrac{\pi }{4} + \pi k\,}\end{array}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,} \right.\dfrac{\pi }{4} + \dfrac{{\pi k}}{2},\,\,\,\,\,\,\,\,\,k\, \in \,Z.\)

Ответ:  \(\dfrac{\pi }{4} + \dfrac{{\pi k}}{2};\quad k \in Z.\)