Đáp án:
A
Giải thích các bước giải:
Ta có:
$\begin{array}{l}
\sin \left( {{x^2} - 2x} \right) = 1\\
\Leftrightarrow {x^2} - 2x = \dfrac{\pi }{2} + k2\pi \left( {k \in Z} \right)\left( 1 \right)\\
x \in \left( {0;\pi } \right) \Rightarrow \left\{ \begin{array}{l}
0 < {x^2} < {\pi ^2}\\
- 2\pi < - 2x < 0
\end{array} \right. \Rightarrow - 2\pi < {x^2} - 2x < {\pi ^2}\left( 2 \right)\\
\left( 1 \right),\left( 2 \right) \Rightarrow \left[ \begin{array}{l}
{x^2} - 2x = \dfrac{{ - 3\pi }}{2}\\
{x^2} - 2x = \dfrac{\pi }{2}\\
{x^2} - 2x = \dfrac{{5\pi }}{2}
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
{x^2} - 2x + \dfrac{{3\pi }}{2} = 0\left( {vn} \right)\\
{x^2} - 2x - \dfrac{\pi }{2} = 0\\
{x^2} - 2x - \dfrac{{5\pi }}{2} = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x \approx 2,603\left( c \right)\\
x \approx - 0.603\left( l \right)\\
x \approx 3,96\left( l \right)\\
x \approx - 1,97\left( l \right)
\end{array} \right. \Leftrightarrow x \approx 2,603\\
\Rightarrow A
\end{array}$
