Toán Lớp 11: giải pt : cot bình x+3cotx+2=0
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Toán Lớp 11: giải pt : cot bình x+3cotx+2=0
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{\cot ^2}x + 3\cot x + 2 = 0\\
\Leftrightarrow \left( {\cot x + 1} \right)\left( {\cot x + 2} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\cot x = – 1\\
\cot x = – 2
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = – \dfrac{\pi }{4} + k\pi \\
x = {\mathop{\rm arccot}\nolimits} \left( { – 2} \right) + k\pi
\end{array} \right.\left( {k \in \mathbb{Z}} \right)
\end{array}$