Giải các phương trình sau a) 3/ 2 − 3 cos 4 x = 6 sin x . sin 3 x ;

a)\(\frac{3}{2} - 3\cos 4x = 6\sin x.\sin 3x\)

\( \Leftrightarrow \frac{3}{2} - 3\cos 4x = 3(\cos 2x - \cos 4x)\)

\( \Leftrightarrow 3\cos 2x = \frac{3}{2}\)

\[ \Leftrightarrow \cos 2x = \frac{1}{2}\,\]

\[ \Leftrightarrow {\mathop{\rm x}\nolimits} = \pm \frac{\pi }{6} + {\mathop{\rm k}\nolimits} \pi ,{\mathop{\rm k}\nolimits} \in \mathbb{Z}\,\].

b) \(\sin 4x + 1 - 2\cos 2x = \sin 2x\)

\( \Leftrightarrow 2\sin 2x.\cos 2x + 1 - 2\cos 2x - \sin 2x = 0\)

\( \Leftrightarrow \left( {\sin 2x - 1} \right)\left( {2\cos 2x - 1} \right) = 0\)

\( \Leftrightarrow \left[ {\begin{array}{*{20}{c}}{\sin 2x = 1}\\{\cos 2x = \frac{1}{2}}\end{array}} \right.\)

\( \Leftrightarrow \left[ {\begin{array}{*{20}{c}}{x = \frac{\pi }{4} + k\pi }\\{x = \pm \frac{\pi }{6} + k\pi }\end{array}\quad \left( {k \in \mathbb{Z}} \right)} \right..\)