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2 câu trả lời 9717
\(\begin{array}{l}
co{t^2}2x - 4cot2x + 3 = 0\\
\Leftrightarrow {\cot ^2}2x - \cot 2x - 3\cot 2x + 3 = 0\\
\Leftrightarrow \cot 2x(\cot 2x - 1) - 3(\cot 2x - 1)) = 0\\
\Leftrightarrow (\cot 2x - 1)(\cot 2x - 3) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\cot 2x - 1 = 0\\
\cot 2x - 3 = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
\cot 2x = 1\\
\cot 2x = 3
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
\tan 2x = 1\\
\tan 2x = \frac{1}{3}
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
2x = \frac{{ \pi }}{4} + k\pi \\
2x = \arctan \frac{1}{3} + k\pi
\end{array} \right.(k \in Z)\\
\Leftrightarrow \left[ \begin{array}{l}
x = \frac{{ \pi }}{8} + \frac{{k\pi }}{2}\\
x = \frac{1}{2}\arctan \frac{1}{3} + \frac{{k\pi }}{2}
\end{array} \right.(k \in Z)
\end{array}\)
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