Giải phương trình: căn bậc hai 3 sinx - cosx = căn bậc hai 2

\(\sqrt 3 \sin x - \cos x = \sqrt 2 \)

\( \Leftrightarrow \frac{{\sqrt 3 }}{2}\sin x - \frac{1}{2}\cos x = \frac{{\sqrt 2 }}{2} \Leftrightarrow \sin \left( {x - \frac{\pi }{6}} \right) = \sin \frac{\pi }{4}\)

\( \Leftrightarrow \left[ {\begin{array}{*{20}{c}}{x - \frac{\pi }{6} = \frac{\pi }{4}}\\{x - \frac{\pi }{6} = \pi - \frac{\pi }{4}}\end{array}} \right. \Leftrightarrow \left[ {\begin{array}{*{20}{c}}{x = \frac{{5\pi }}{{12}} + k2\pi }\\{x = \frac{{11\pi }}{{12}} + k2\pi }\end{array}} \right.\left( {k \in \mathbb{Z}} \right)\)