Giúp em câu này vs ạ: √3 sin(x) +cos(x) =2sin3(x)

Đáp án:

$\left[\begin{array}{l}x = \dfrac{\pi}{12}+ k\pi\\x =\dfrac{5\pi}{24} +k\dfrac{\pi}{2}\end{array}\right.\quad (k\in\Bbb Z)$

Giải thích các bước giải:

$\quad \sqrt3\sin x +\cos x =2\sin3x$

$\to \dfrac{\sqrt3}{2}\sin x +\dfrac12\cos x =\sin3x$

$\to\sin\left(x +\dfrac{\pi}{6}\right) =\sin3x$

$\to \left[\begin{array}{l}x +\dfrac{\pi}{6} = 3x + k2\pi\\x +\dfrac{\pi}{6} = \pi – 3x +k2\pi\end{array}\right.$

$\to \left[\begin{array}{l}x = \dfrac{\pi}{12}+ k\pi\\x =\dfrac{5\pi}{24} +k\dfrac{\pi}{2}\end{array}\right.\quad (k\in\Bbb Z)$