\({\sin ^2}x + 2{\cos ^2}x = 3\sin x\cos x.\)
A.\(\left[ \begin{array}{l}x = \arctan 2 + k2\pi \\x = \frac{\pi }{4} + k2\pi \end{array} \right.\,\,\,\,\left( {k \in \mathbb{Z}} \right)\)
B.\(\left[ \begin{array}{l}x = \arctan 2 + k2\pi \\x = - \frac{\pi }{4} + k2\pi \end{array} \right.\,\,\,\,\left( {k \in \mathbb{Z}} \right)\)
C.\(\left[ \begin{array}{l}x = \arctan 2 + k\pi \\x = \frac{\pi }{4} + k\pi \end{array} \right.\,\,\,\,\left( {k \in \mathbb{Z}} \right)\)
D.\(\left[ \begin{array}{l}x = \arctan 2 + k\pi \\x = - \frac{\pi }{4} + k\pi \end{array} \right.\,\,\,\,\left( {k \in \mathbb{Z}} \right)\)