PT
$\Leftrightarrow \cos x + \cos 5x +\cos 3x + \cos 5x =0$
$\Leftrightarrow 2\cos 3x\cos 2x +2\cos 4x\cos x =0$
$\Leftrightarrow \cos 3x\cos 2x +\cos 4x\cos x =0$
Đặt $t=\cos x$ thì $\cos 2x=2t^2-1,\cos 3x = 4t^3-3t, \cos 4x=2\cos^22x-1=2(2t^2-1)^2-1.$ PT
$\Leftrightarrow (4t^3-3t)(2t^2-1)+ t\left[ {2(2t^2-1)^2-1} \right]=0$
$\Leftrightarrow 16t^5-18t^3+4t=0$
$\Leftrightarrow \left[ {\begin{matrix} t=0\\ t=\pm\frac{\sqrt{9\pm\sqrt{17}}}{4}\end{matrix}} \right.$