Đáp án:
$\begin{array}{l}
\cos x + \cos 2x + \cos 3x + \cos 4x = \frac{3}{2}\\
\Leftrightarrow \cos x + \cos 4x + \cos 2x + \cos 3x = \frac{3}{2}\\
\Leftrightarrow 2\cos \frac{{5x}}{2}.\cos \frac{{3x}}{2} + 2\cos \frac{{5x}}{2}.\cos \frac{x}{2} = \frac{3}{2}\\
\Leftrightarrow 2\cos \frac{{5x}}{2}.\left( {\cos \frac{{3x}}{2} + \cos \frac{x}{2}} \right) = \frac{3}{2}\\
\Leftrightarrow 2.\cos \frac{{5x}}{2}.2.\cos x.\cos \frac{x}{2} = \frac{3}{2}\\
\Leftrightarrow 2.\cos \frac{{5x}}{2}.\cos x.2.\cos \frac{x}{2}.\sin \frac{x}{2} = \frac{3}{2}\sin \frac{x}{2}\\
\Leftrightarrow 2.\cos \frac{{5x}}{2}.\cos x.\sin x = \frac{3}{2}.\sin \frac{x}{2}\\
\Leftrightarrow \cos \frac{{5x}}{2}.\sin 2x = \frac{3}{2}\sin \frac{x}{2}\\
\Leftrightarrow 2\cos \frac{{5x}}{2}.\sin 2x = 3\sin \frac{x}{2}\\
\Leftrightarrow x \in \emptyset
\end{array}$
Vậy không có giá trị của x để thỏa mãn phương trình.
