Phương trình \(\sqrt 2 {\ma...

C

- Hướng dẫn giải

Ta có: \(\sqrt 2 \sin x - \sqrt 2 \cos x = \sqrt 3 \)

\(\begin{array}{l}\Leftrightarrow \sqrt 2 \left( {\sin x - \cos x} \right) = \sqrt 3 \\\Leftrightarrow \sqrt 2 .\sqrt 2 \sin \left( {x - \frac{\pi }{4}} \right) = \sqrt 3\end{array}\)

\(\Leftrightarrow 2\sin \left( {x - \dfrac{\pi }{4}} \right) = \sqrt 3 \)

\(\Leftrightarrow \sin \left( {x - \dfrac{\pi }{4}} \right) = \dfrac{{\sqrt 3 }}{2}\)\( \Leftrightarrow \sin \left( {x - \dfrac{\pi }{4}} \right) = \sin \dfrac{\pi }{3}\)

\(\Leftrightarrow \left[ \begin{array}{l}x - \dfrac{\pi }{4} = \dfrac{\pi }{3} + k2\pi \\x - \dfrac{\pi }{4} = \pi- \dfrac{\pi }{3} + k2\pi \end{array} \right. \)\(\Leftrightarrow \left[ \begin{array}{l}x = \dfrac{{7\pi }}{{12}} + k2\pi \\x = \dfrac{11\pi }{{12}} + k2\pi \end{array} \right.\,\left( {k \in \mathbb{Z}} \right)\)