Cho biết cosα = \(\frac{{ - 2}}{3}.\) Giá trị của P = \(\frac{{\cot \alpha + 3\tan \alpha }}{{2\cot \alpha + \tan \alpha }}\) bằng bao nhiêu?

P = \(\frac{{\cot \alpha + 3\tan \alpha }}{{2\cot \alpha + \tan \alpha }}\)

\[ = \frac{{\frac{{\cos \alpha }}{{\sin \alpha }} + 3\frac{{\sin \alpha }}{{\cos \alpha }}}}{{2\frac{{\cos \alpha }}{{\sin \alpha }} + \frac{{\sin \alpha }}{{\cos \alpha }}}} = \frac{{{{\cos }^2}\alpha + 3{{\sin }^2}\alpha }}{{2{{\cos }^2}\alpha + {{\sin }^2}\alpha }} = \frac{{{{\left( {\frac{{ - 2}}{3}} \right)}^2} + 3.\frac{5}{9}}}{{2.{{\left( {\frac{{ - 2}}{3}} \right)}^2} + \frac{5}{9}}} = \frac{{19}}{{13}}\].