mọi người cho mình hỏi câu này với ạ. mình cảm ơn
\(\Leftrightarrow sin2x=-sinx\)
\(\Leftrightarrow sin2x=sin\left(-x\right)\)
\(\Rightarrow\left[{}\begin{matrix}sin2x=-x+k2\pi\\sin2x=\pi+x+n2\pi\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}3x=k2\pi\\x=\pi+n2\pi\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{k2\pi}{3}\\x=\pi+n2\pi\end{matrix}\right.\)
\(0\le x\le2\pi\Rightarrow\left\{{}\begin{matrix}0\le\dfrac{k2\pi}{3}\le2\pi\\0\le\pi+n2\pi\le2\pi\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}0\le k\le3\\-\dfrac{1}{2}\le n\le\dfrac{1}{2}\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}k=\left\{0;1;2;3\right\}\\n=0\end{matrix}\right.\)
\(\Rightarrow x=\left\{0;\dfrac{2\pi}{3};\dfrac{4\pi}{3};2\pi;\pi\right\}\Rightarrow0+\dfrac{2\pi}{3}+\dfrac{4\pi}{3}+2\pi+\pi=5\pi\)
