$pt\Leftrightarrow (\cos^3x+3\cos x)-4(\cos 2x+1)=0⇔4cos3x−4.2cos2x=0\Leftrightarrow \cos^3x-2\cos^2x=0\Leftrightarrow \left[ cosx=0cosx=2 \right.\Leftrightarrow x=k\pi -\frac{\pi}2(k \in \mathbb{Z})Do0 \le x \le 15\Leftrightarrow 0 \le k\pi -\frac{\pi}2 \le 15\Leftrightarrow \frac 12 \le k \le \frac{15}{\pi}+\frac 12Dok\in \mathbb{Z}\Rightarrow 1 \le k \le 5Do đó S=\left\{\frac{\pi}{2};\frac{3\pi}{2};\frac{5\pi}{2};\frac{7\pi}{2};\frac{9\pi}{2} \right\}$
pt\Leftrightarrow (\cos3x+3\cos x)-4(\cos 2x+1)=0\Leftrightarrow 4\cos^3x-4.2\cos^2x=0\Leftrightarrow \cos^3x-2\cos^2x=0\Leftrightarrow \left[ \begin{array}{l} \cos x=0\\ \cos x=2 \end{array} \right.\Leftrightarrow x=k\pi -\frac{\pi}2(k \in \mathbb{Z})Do
0 \le x \le 15\Leftrightarrow 0 \le k\pi -\frac{\pi}2 \le 15\Leftrightarrow \frac 12 \le k \le \frac{15}{\pi}+\frac 12Do
k\in \mathbb{Z}\Rightarrow 1 \le k \le 5Do đó
S=\left\{\frac{\pi}{2};\frac{3\pi}{2};\frac{5\pi}{2};\frac{7\pi}{2};\frac{9\pi}{2} \right\}