Đáp án đúng: C
Giải chi tiết:Điều kiện:\(\cos \left( {x + \frac{\pi }{6}} \right) \ne 0 \Leftrightarrow x + \frac{\pi }{6} \ne \frac{\pi }{2} + k\pi \Leftrightarrow x \ne \frac{\pi }{3} + k\pi \,(k \in \mathbb{Z}).\)
\(\begin{array}{l}\,\,\,\,\,\sqrt 3 .\,\tan \left( {x + \frac{\pi }{6}} \right) - 3 = 0 \Leftrightarrow \tan \left( {x + \frac{\pi }{6}} \right) = \sqrt 3 = tan\frac{\pi }{3}\\ \Leftrightarrow x + \frac{\pi }{6} = \frac{\pi }{3} + k\pi \,\,\,(k \in \mathbb{Z}) \Leftrightarrow x = \frac{\pi }{6} + k\pi \,\;\;\left( {tm} \right)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(k \in \mathbb{Z}).\end{array}\)
Chọn C.