$\cos2x-\cos x=0$
$\Leftrightarrow 2\cos^2x-\cos x-1=0$
$\Leftrightarrow \cos x=1$, $\cos x=-0,5$
$+] \cos x=1\Leftrightarrow x=k2\pi$
$\Rightarrow 0\le k2\pi\le 4\pi\Leftrightarrow 0\le k\le 2$
$\Rightarrow k\in\{0;1;2\}$
$+] \cos x=-0,5\Leftrightarrow x=\pm\dfrac{2\pi}{3}+k2\pi$
$0\le \dfrac{2\pi}{3}+k2\pi\le 4\pi\Leftrightarrow -0,33\le k\le 1,67\Rightarrow k\in\{0;1\}$
$0\le -\dfrac{2\pi}{3}+k2\pi\le 4\pi\Leftrightarrow 0,3\le k\le 2,3\Rightarrow k\in\{1;2\}$
Vậy có tất cả 7 nghiệm.
Hay nhất
Chọn B
Ta có \[cos^{2} x+cosx=0\Leftrightarrow \left[\begin{array}{l} {cosx=0} \\ {cosx=-1} \end{array}\right. \Leftrightarrow \left[\begin{array}{l} {x=\frac{\pi }{2} +k\pi } \\ {x=\pi +k2\pi } \end{array}\right. {\rm \; \; }[k\in {\rm Z}].\]
Vì với \[k\in {\rm Z}: \frac{\pi }{2}