Phương trình \(2\sin \left(...

D

- Hướng dẫn giải

Ta có: 

\(2\sin \left( {2x + \dfrac{\pi }{4}} \right) = 1\\ \Leftrightarrow \sin \left( {2x + \dfrac{\pi }{4}} \right) = \dfrac{1}{2}\)

\(\Leftrightarrow \left[ \begin{array}{l}2x + \dfrac{\pi }{4} = \dfrac{\pi }{6} + k2\pi \\2x + \dfrac{\pi }{4} = \pi - \dfrac{\pi }{6} + k2\pi \end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}x = - \dfrac{\pi }{{24}} + k\pi \\x = \dfrac{{7\pi }}{{24}} + k\pi \end{array} \right.\,\left( {k \in \mathbb{Z}} \right)\)