\({\sin ^2}x + 2{\cos ^2}x = 3\sin x\cos x.\)

Câu hỏi: \({\sin ^2}x + 2{\cos ^2}x = 3\sin x\cos x.\)

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 \(\left[ \begin{array}{l}x = \arctan 2 + k\pi \\x =  - \frac{\pi }{4} + k\pi \end{array} \right.\,\,\,\,\left( {k \in \mathbb{Z}} \right)\)