Toán Lớp 11: Y=tan x + cotx/cot²x -1.tìm tập xác định
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Toán Lớp 11: Y=tan x + cotx/cot²x -1.tìm tập xác định
Comments ( 1 )
Dkxd:\left\{ \begin{array}{l}
\sin x \ne 0\\
\cos x \ne 0\\
{\cot ^2}x \ne 1
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
2.\sin x.\cos x \ne 0\\
\cot x \ne 1\\
\cot x \ne – 1
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\sin 2x \ne 0\\
x \ne \dfrac{\pi }{4} + k\pi \\
x \ne – \dfrac{\pi }{4} + k\pi
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
2x \ne k\pi \\
x \ne \pm \dfrac{\pi }{4} + k\pi
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x \ne \dfrac{{k\pi }}{2}\\
x \ne \pm \dfrac{\pi }{4} + k\pi
\end{array} \right.\\
Vậy\,TXD:D = R\backslash \left\{ {\dfrac{{k\pi }}{2}; \pm \dfrac{\pi }{4} + k\pi /k \in Z} \right\}
\end{array}$