Ta có: \(\tan \alpha = \sqrt 2 \)\( \Rightarrow \dfrac{{\sin \alpha }}{{\cos \alpha }} = \sqrt 2 \) \( \Rightarrow \sin \alpha = \sqrt 2 \cos \alpha \)
\( \Rightarrow A = \dfrac{{3\sqrt 2 \cos \alpha - \cos \alpha }}{{\sqrt 2 \cos \alpha + \cos \alpha }}\) \( = \dfrac{{\cos \alpha \left( {3\sqrt 2 - 1} \right)}}{{\cos \alpha \left( {\sqrt 2 + 1} \right)}} = \dfrac{{3\sqrt 2 - 1}}{{\sqrt 2 + 1}}\) \( = \dfrac{{\left( {3\sqrt 2 - 1} \right)\left( {\sqrt 2 - 1} \right)}}{{\left( {\sqrt 2 + 1} \right)\left( {\sqrt 2 - 1} \right)}}\) \( = \dfrac{{6 - 4\sqrt 2 + 1}}{{2 - 1}} = 7 - 4\sqrt 2 \)
Vậy \(A = 7 - 4\sqrt 2 \).
