Задача 17. Решите уравнение: \({\text{t}}{{\text{g}}^2}x = 3\)
ОТВЕТ: \( \pm \dfrac{\pi }{3} + \pi k;\quad \,k \in Z.\)Ответ
\({\rm{t}}{{\rm{g}}^2}x = 3\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{{\rm{tg}}\,x = \sqrt 3 ,\,\,}\\{{\rm{tg}}\,x = -\sqrt 3 }\end{array}\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = \dfrac{\pi }{3} + \pi k,\,\,\,\,}\\{x = -\dfrac{\pi }{3} + \pi k\,}\end{array}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,} \right.} \right.x = \pm \dfrac{\pi }{3} + \pi k,\,\,\,\,\,\,\,\,k\, \in \,Z.\) Ответ: \( \pm \dfrac{\pi }{3} + \pi k;\quad \,k \in Z.\)Решение