Задание
Прочитай теоретическую справку и заполни пропуски
Пример.
Реши уравнение \(\tg x -2\ctg x+1=0\) .
Решение.
\(\ctg x =\dfrac1{\tg x}\)
\(\tg x -\dfrac2{\tg x}+1=0\space|\cdot \tg x\)
\(\tg^2x+\tg x-2=0\)
\(\left[\begin{aligned} \tg x= 1\\ \tg x=-2\end{aligned}\right.\Rightarrow\) \(\left[\begin{aligned} x\_1= \dfrac{\pi}4+\pi n,\,\text{где } n\in\mathbb{Z}\\ x\_2=- \arctg 2+\pi m,\,\text{где } m\in\mathbb{Z}\end{aligned}\right.\)
- \(\arctg 2\)
- \(-\arctg 2\)
- \(\pm \arctg 2\)
- \(\dfrac{\pi}{4}\)
- \(-\dfrac{\pi}{4}\)
- \(\pm \dfrac{\pi}{4}\)
- \(\pi n\)
- \(\pi m\)
- \(2\pi n\)
Ответ:
\(x\_1=\) [ ] \(+\) [ ] \(,\space n\in\mathbb{Z}\)
\(x\_2=\) [ ] \(+\) [ ] \(,\space m\in\mathbb{Z}\)