2 câu trả lời
Đáp án: $$x = \frac{{7\pi }}{{60}} + \frac{{2k\pi }}{5}\,hoặc\,x = \frac{{ - 11\pi }}{{60}} + \frac{{2k\pi }}{5}$$
Giải thích các bước giải:
$\eqalign{ & \sqrt 3 \cos 5x - \sin 5x = - \sqrt 2 \cr & \Leftrightarrow \frac{{\sqrt 3 }}{2}\cos 5x + \frac{{ - 1}}{2}\sin 5x = - \frac{{\sqrt 2 }}{2} \cr & \Leftrightarrow \cos \frac{{ - \pi }}{6}.\cos 5x + \sin \frac{{ - \pi }}{6}.\sin 5x = - \frac{{\sqrt 2 }}{2} \cr & \Leftrightarrow \cos (5x + \frac{\pi }{6}) = \cos \frac{{3\pi }}{4} \cr & \Leftrightarrow 5x + \frac{\pi }{6} = \pm \frac{{3\pi }}{4} + 2k\pi \cr & \Leftrightarrow x = \frac{{7\pi }}{{60}} + \frac{{2k\pi }}{5}\,hoặc\,x = \frac{{ - 11\pi }}{{60}} + \frac{{2k\pi }}{5} \cr} $
