$3cos3x.cosx+ \sqrt{3}(1+sin2x) = 2\sqrt{3}cos^{2}(2x+\frac{\pi }{4})$
$\Leftrightarrow 3\cos 3x \cos x+ \sqrt{3}(1+sin2x)=\sqrt 3 (1-\cos (4x+\dfrac{\pi }{2})$
$\Leftrightarrow 3\cos 3x \cos x +\sqrt 3 \sin 2x = -\sqrt 3 \sin 4x$
$\Leftrightarrow 3\cos 3x \cos x +\sqrt 3(\sin 2x +\sin 4x) = 0$
$\Leftrightarrow 3\cos 3x \cos x + 2\sqrt 3 \sin 3x \cos x = 0$
$\Leftrightarrow \cos x (3\cos 3x + 2\sqrt 3 \sin 3x) =0$ dễ rồi tự làm nhé