\(\begin{array}{l} a.A = \dfrac{{\dfrac{{{{\cos }^2}x + {{\sin }^2}x}}{{\sin x.\cos x}}}}{{\dfrac{{{{\cos }^2}x - {{\sin }^2}x}}{{\sin x.\cos x}}}} = \dfrac{{{{\cos }^2}x + {{\sin }^2}x}}{{{{\cos }^2}x - {{\sin }^2}x}}\\  = \dfrac{1}{{(1 - {{\sin }^2}x) - {{\sin }^2}x}} = \dfrac{25}{7}\\ g.G = \dfrac{{\dfrac{{\cos x}}{{\sin x}} + \dfrac{{3\sin x}}{{\cos x}}}}{{2.\dfrac{{\cos x}}{{\sin x}} + \dfrac{{\sin x}}{{\cos x}}}} = \dfrac{{{{\cos }^2}x + 3(1 - {{\cos }^2}x)}}{{\sin x.\cos x}}.\dfrac{{\sin x.\cos x}}{{2{{\cos }^2}x + 1 - {{\cos }^2}x}}\\  = \dfrac{{ - 2{{\cos }^2}x + 3}}{{{{\cos }^2}x + 1}} = \dfrac{{19}}{{13}} \end{array}\)

\(\begin{array}{l} b.{\sin ^2}a + {\cos ^2}a = 1\\  \to \dfrac{1}{9} + {\cos ^2}a = 1\\  \to {\cos ^2}a = \dfrac{8}{9}\\ Do:a \in \left( {\dfrac{\pi }{2};\pi } \right)\\  \to \cos a < 0\\  \to \cos a =  - \dfrac{{2\sqrt 2 }}{3}\\  \to \tan a = \dfrac{{\sin a}}{{\cos a}} =  - \dfrac{{\sqrt 2 }}{4}\\  \to \cot a =  - 2\sqrt 2 \\ B = \dfrac{{8{{\tan }^2}a + 3\cot a - 1}}{{\tan a + \cot a}}\\  = \dfrac{{8.{{\left( { - \dfrac{{\sqrt 2 }}{4}} \right)}^2} + 3.\left( { - 2\sqrt 2 } \right) - 1}}{{ - \dfrac{{\sqrt 2 }}{4} - 2\sqrt 2 }} = \dfrac83\\ c.\cot a =  - 3\\  \to \dfrac{{\cos a}}{{\sin a}} =  - 3\\  \to \cos a =  - 3\sin a\\  \to C =\dfrac{\sin^2a+2\sin a(-3\sin a)-2.(-3\sin a)^2}{2\sin^2a-3\sin a(-3\sin a)+4(-3\sin a)^2}\\ =\dfrac{-23\sin^2a}{47\sin^2a}=\dfrac{-23}{47}\\   d.\tan a = 2\\  \to \dfrac{{\sin a}}{{\cos a}} = 2\\  \to \sin a = 2\cos a\\  \to D = \dfrac{{2\cos a + 5\cos a}}{{8{{\cos }^3}a - 2{{\cos }^3}a}}\\  = \dfrac{{7\cos a}}{{6{{\cos }^3}a}}\\  = \dfrac{7}{{6{{\cos }^2}a}}\\ Có:\sin {a^2} + {\cos ^2}a = 1\\  \to 4{\cos ^2}a + {\cos ^2}a = 1\\  \to 5{\cos ^2}a = 1\\  \to {\cos ^2}a = \dfrac{1}{5}\\  \to D = \dfrac{7}{{6.\dfrac{1}{5}}} = \dfrac{{35}}{6}\\ e.\tan a = 2\\  \to \dfrac{{\sin a}}{{\cos a}} = 2\\  \to \sin a = 2\cos a\\  \to E = \dfrac{{8{{\cos }^3}a - 2.8{{\cos }^3}a + \cos a}}{{2\cos a - 8{{\cos }^3}a}}\\  = \dfrac{{ - 8{{\cos }^3}a + \cos a}}{{2\cos a - 8{{\cos }^3}a}}\\  = \dfrac{{ - 8{{\cos }^2}a + 1}}{{2 - 8{{\cos }^2}a}}\\ Có:{\cos ^2}a + {\sin ^2}a = 1\\  \to {\cos ^2}a + 4{\cos ^2}a = 1\\  \to {\cos ^2}a = \dfrac{1}{5}\\  \to E = \dfrac{{ - 8.\dfrac{1}{5} + 1}}{{2 - 8.\dfrac{1}{5}}} =  - \dfrac{3}{2} \end{array}\)