\(\Leftrightarrow sin\left(4x-\dfrac{\pi}{5}\right)=sin\left(-\dfrac{\pi}{4}\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}4x-\dfrac{\pi}{5}=-\dfrac{\pi}{4}+k2\pi\\4x-\dfrac{\pi}{5}=\dfrac{5\pi}{4}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}4x=-\dfrac{\pi}{20}+k2\pi\\4x=\dfrac{29\pi}{20}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{\pi}{80}+\dfrac{k\pi}{2}\\x=\dfrac{29\pi}{80}+\dfrac{k\pi}{2}\end{matrix}\right.\) (\(k\in Z\))
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