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Câu hỏi: Tập tất cả các nghiệm của phương trình ${2\sin 2x+1=0}$ là
A. ${S=\left\{ -\dfrac{\pi }{6}+k\pi ,\dfrac{7\pi }{12}+k\pi ,k\in \mathbb{Z} \right\}}$.
B. ${S=\left\{ -\dfrac{\pi }{12}+k2\pi ,\dfrac{7\pi }{12}+k2\pi ,k\in \mathbb{Z} \right\}}$.
C. ${S=\left\{ -\dfrac{\pi }{6}+k2\pi ,\dfrac{7\pi }{12}+k2\pi ,k\in \mathbb{Z} \right\}}$.
D. ${S=\left\{ -\dfrac{\pi }{12}+k\pi ,\dfrac{7\pi }{12}+k\pi ,k\in \mathbb{Z} \right\}}$.
A. ${S=\left\{ -\dfrac{\pi }{6}+k\pi ,\dfrac{7\pi }{12}+k\pi ,k\in \mathbb{Z} \right\}}$.
B. ${S=\left\{ -\dfrac{\pi }{12}+k2\pi ,\dfrac{7\pi }{12}+k2\pi ,k\in \mathbb{Z} \right\}}$.
C. ${S=\left\{ -\dfrac{\pi }{6}+k2\pi ,\dfrac{7\pi }{12}+k2\pi ,k\in \mathbb{Z} \right\}}$.
D. ${S=\left\{ -\dfrac{\pi }{12}+k\pi ,\dfrac{7\pi }{12}+k\pi ,k\in \mathbb{Z} \right\}}$.
Phươngtrình$2\sin 2x+1=0\Leftrightarrow \sin 2x=-\dfrac{1}{2}=\sin \left( -\dfrac{\pi }{6} \right)\Leftrightarrow \left[ \begin{array}{*{35}{l}}
2x=-\dfrac{\pi }{6}+k2\pi \\
2x=\dfrac{7\pi }{6}+k2\pi \\
\end{array}\Leftrightarrow \left[ \begin{array}{*{35}{l}}
x=-\dfrac{1}{12}+k\pi \\
x=\dfrac{7\pi }{12}+k\pi \\
\end{array}\quad \right. \right. $(vớ$ k\in \mathbb{Z})$
2x=-\dfrac{\pi }{6}+k2\pi \\
2x=\dfrac{7\pi }{6}+k2\pi \\
\end{array}\Leftrightarrow \left[ \begin{array}{*{35}{l}}
x=-\dfrac{1}{12}+k\pi \\
x=\dfrac{7\pi }{12}+k\pi \\
\end{array}\quad \right. \right. $(vớ$ k\in \mathbb{Z})$
Đáp án D.