Đáp án:
Giải thích các bước giải:
\[\begin{array}{l}
\sin 2x = \frac{{ - 1}}{2}\\
\Leftrightarrow \left[ \begin{array}{l}
2x = \frac{{ - \pi }}{6} + k2\pi \\
2x = \frac{{7\pi }}{6} + k2\pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \frac{{ - \pi }}{{12}} + k\pi \\
x = \frac{{7\pi }}{{12}} + k\pi
\end{array} \right.\\
Neu\,x = \frac{{ - \pi }}{{12}} + k\pi \,thi\,0 < x < \pi \Leftrightarrow 0 < \frac{{ - \pi }}{{12}} + k\pi < \pi \\
\Leftrightarrow \frac{1}{2} < k < \frac{{13}}{{12}} \Rightarrow k = 1 \Rightarrow x = \frac{{11\pi }}{{12}}\\
Neu\,x = \frac{{7\pi }}{{12}} + k\pi \,thi\,0 < x < \pi \Leftrightarrow 0 < \frac{{7\pi }}{{12}} + k\pi < \pi \\
\Leftrightarrow \frac{{ - 7}}{{12}} < k < \frac{5}{{12}} \Rightarrow k = 0 \Rightarrow x = \frac{{7\pi }}{{12}}\\
Vay\,co\,2\,nghiem.
\end{array}\]
