\textbf{109-} The general solution of the trigonometric equation $2\sqrt{2}\sin x \cos x = \sin x + \cos x$ is which of the following?
\begin{itemize}
\item[(1)] $k\pi + \dfrac{\pi}{4}$
\item[(2)] $\dfrac{2k\pi}{3} - \dfrac{\pi}{4}$
\item[(3)] $\dfrac{2k\pi}{3} + \dfrac{\pi}{4}$
\item[(4)] $2k\pi \pm \dfrac{\pi}{4}$
\end{itemize}
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