Уравнения, сводящиеся к простейшим заменой неизвестного. Задача 12

ОТВЕТ: \( \pm \dfrac{\pi }{3} + \pi k;\quad \,k \in Z.\)

\({\cos ^2}x = \dfrac{1}{4}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{\cos x = \dfrac{1}{2},}\\{\cos x = -\dfrac{1}{2}}\end{array}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x =  \pm \dfrac{\pi }{3} + 2\pi k,\,\,\,\,}\\{x =  \pm \dfrac{{2\pi }}{3} + 2\pi k\,}\end{array}\,\,\,\,} \right.} \right.\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,x =  \pm \dfrac{\pi }{3} + \pi k,\,\,\,\,\,\,\,\,k\, \in \,Z.\)

Ответ:  \( \pm \dfrac{\pi }{3} + \pi k;\quad \,k \in Z.\)