Đáp án:
$S =\left\{\dfrac{\pi}{4} + k\pi;\ \arctan2 + k\pi\ \Bigg|\ k\in\Bbb Z\right\}$
Giải thích các bước giải:
$\quad \tan x + 2\cot x - 3 = 0\qquad (*)$
ĐK: $x \ne \dfrac{n\pi}{2}$
$(*)\Leftrightarrow \tan^2x - 3\tan x + 2 = 0$
$\Leftrightarrow (\tan x -1)(\tan x -2)= 0$
$\Leftrightarrow \left[\begin{array}{l}\tan x = 1\\\tan x = 2\end{array}\right.$
$\Leftrightarrow \left[\begin{array}{l}x =\dfrac{\pi}{4} + k\pi\\x = \arctan2 + k\pi\end{array}\right.\quad (k\in\Bbb Z)$
Vậy $S =\left\{\dfrac{\pi}{4} + k\pi;\ \arctan2 + k\pi\ \Bigg|\ k\in\Bbb Z\right\}$
