\(2cos\left(2x-\dfrac{\pi}{3}\right)+\sqrt{2}=0\)
\(\Leftrightarrow cos\left(2x-\dfrac{\pi}{3}\right)=-\dfrac{\sqrt{2}}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-\dfrac{\pi}{3}=\dfrac{3\pi}{4}+k2\pi\\2x-\dfrac{\pi}{3}=-\dfrac{3\pi}{4}+k2\pi\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{13\pi}{24}+k\pi\\x=-\dfrac{5\pi}{24}+k\pi\end{matrix}\right.\)
\(tan\left(\dfrac{\pi}{4}-2x\right)-\sqrt{3}=0\)
\(\Leftrightarrow tan\left(2x-\dfrac{\pi}{4}\right)=-\sqrt{3}\)
\(\Leftrightarrow2x-\dfrac{\pi}{4}=-\dfrac{\pi}{3}+k\pi\)
\(\Rightarrow x=-\dfrac{\pi}{24}+\dfrac{k\pi}{2}\)
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