Toán Lớp 11: cot bình x/2=1/3 help me please
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Toán Lớp 11: cot bình x/2=1/3 help me please
Comments ( 1 )
x = \dfrac{{2\pi }}{3} + k2\pi \\
x = – \dfrac{{2\pi }}{3} + k2\pi
\end{array} \right.\,\,\,\,\left( {k \in Z} \right)\)
{\cot ^2}\dfrac{x}{2} = \dfrac{1}{3}\\
\Leftrightarrow \left[ \begin{array}{l}
\cot \dfrac{x}{2} = \dfrac{{\sqrt 3 }}{3}\\
\cot \dfrac{x}{2} = – \dfrac{{\sqrt 3 }}{3}
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
\cot \dfrac{x}{2} = \cot \dfrac{\pi }{3}\\
\cot \dfrac{x}{2} = \cot \dfrac{{ – \pi }}{3}
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
\dfrac{x}{2} = \dfrac{\pi }{3} + k\pi \\
\dfrac{x}{2} = – \dfrac{\pi }{3} + k\pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{{2\pi }}{3} + k2\pi \\
x = – \dfrac{{2\pi }}{3} + k2\pi
\end{array} \right.\,\,\,\,\left( {k \in Z} \right)
\end{array}\)