Giải phương trình: ${\tan ^2}x = 3$ có nghiệm là
A. ${\rm{x}} = - \frac{\pi }{3} + k\pi .$
B. ${\rm{x}} = \pm \frac{\pi }{3} + k\pi .$
C. vô nghiệm.
D. ${\rm{x}} = \frac{\pi }{3} + k\pi .$
A. ${\rm{x}} = - \frac{\pi }{3} + k\pi .$
B. ${\rm{x}} = \pm \frac{\pi }{3} + k\pi .$
C. vô nghiệm.
D. ${\rm{x}} = \frac{\pi }{3} + k\pi .$
Chọn B.
Ta có: ${\tan ^2}x = 3 \Leftrightarrow \left[ \begin{array}{l}\tan x = \sqrt 3 \\\tan x = - \sqrt 3 \end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = \frac{\pi }{3} + k\pi \\x = - \frac{\pi }{3} + k\pi \end{array} \right.,\left( {k \in \mathbb{Z}} \right).$
Ta có: ${\tan ^2}x = 3 \Leftrightarrow \left[ \begin{array}{l}\tan x = \sqrt 3 \\\tan x = - \sqrt 3 \end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = \frac{\pi }{3} + k\pi \\x = - \frac{\pi }{3} + k\pi \end{array} \right.,\left( {k \in \mathbb{Z}} \right).$