Đáp án:
$2$ nghiệm
Giải thích các bước giải:
$\quad \cos x =\dfrac13$
$\to \left[\begin{array}{l}x = \arccos\dfrac13 + k2\pi\\x = -\arccos\dfrac13 + k2\pi\end{array}\right.\quad (k\in\Bbb Z)$
Ta lại có:
$\quad 0 < x <2\pi$
$\to \left[\begin{array}{l}0 < \arccos\dfrac13 + k2\pi< 2\pi\\0 < -\arccos\dfrac13 + k2\pi < 2\pi\end{array}\right.$
$\to \left[\begin{array}{l}-\dfrac{1}{2\pi}\cdot\arccos\dfrac13 < k < 1 -\dfrac{1}{2\pi}\cdot\arccos\dfrac13\\\dfrac{1}{2\pi}\cdot\arccos\dfrac13 < k < 1 +\dfrac{1}{2\pi}\cdot\arccos\dfrac13\end{array}\right.$
$\to\left[\begin{array}{l}-0,2 < k < 0,8\\0,2< k < 1,2\end{array}\right.$
$\to \left[\begin{array}{l}k = 0\\k = 1\end{array}\right.$
$\to 2$ nghiệm
