Задача 10. Решите уравнение:    \({\cos ^2}x-1 = 0\)

Ответ

ОТВЕТ: \(\pi k;\,\,\,\,\,k \in Z.\)

Решение

\({\cos ^2}x-1 = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,1-{\cos ^2}x = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{\sin ^2}x = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\sin x = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,x = \pi k,\,\,\,\,\,\,\,\,\,\,\,k\, \in \,Z.\)

Ответ:  \(\pi k;\,\,\,\,\,k \in Z.\)