Đáp án:$m = 0\,hoặc\,m \ge \frac{3}{4}$
Giải thích các bước giải:
$\begin{array}{l}
- \frac{\pi }{2} < x < \frac{\pi }{2}\\
\Rightarrow - \pi < 2x < \pi \\
\Rightarrow - 1 \le \sin 2x \le 1\\
m{\sin ^2}2x - \left( {2m - 3} \right)\sin 2x - 3\left( {m - 1} \right) = 0\\
\Rightarrow m{t^2} - \left( {2m - 3} \right)t - 3m + 3 = 0\left( { - 1 \le t \le 1} \right)\\
\Rightarrow m{t^2} + mt - 3\left( {m - 1} \right)t - 3\left( {m - 1} \right) = 0\\
\Rightarrow \left( {t + 1} \right)\left( {mt - 3m + 3} \right) = 0\\
\Rightarrow \left[ \begin{array}{l}
t = - 1\left( {tm} \right)\\
mt = 3m - 3\left( * \right)
\end{array} \right.\\
(*) \Rightarrow \left[ \begin{array}{l}
m = 0\\
\left\{ \begin{array}{l}
m \ne 0\\
- 1 \le \frac{{3m - 3}}{m} \le 1
\end{array} \right.
\end{array} \right. \Rightarrow \left[ \begin{array}{l}
m = 0\\
\left\{ \begin{array}{l}
m \ne 0\\
m \ge \frac{3}{4}
\end{array} \right.
\end{array} \right. \Rightarrow \left[ \begin{array}{l}
m = 0\\
m \ge \frac{3}{4}
\end{array} \right.
\end{array}$
