$\begin{array}{l} \left( {2\cos x - 1} \right)\sin \left( {x + \dfrac{\pi }{4}} \right) = 0\\ \Leftrightarrow \left[ \begin{array}{l} \cos x = \dfrac{1}{2}\\ \sin \left( {x + \dfrac{\pi }{4}} \right) = 0 \end{array} \right.\\ \Leftrightarrow \left[ \begin{array}{l} x = \pm \dfrac{\pi }{3} + k2\pi \\ x + \dfrac{\pi }{4} = k\pi \end{array} \right.\\ \Leftrightarrow \left[ \begin{array}{l} x = \pm \dfrac{\pi }{3} + k2\pi \\ x = - \dfrac{\pi }{4} + k\pi \end{array} \right.\left( {k \in Z} \right) \end{array}$
