Cho cos A = -2/3 . Tính giá trị biểu thức E = cot a+ 3tan a / 2cot a + tan a

$@meo$

`E = (cot a+ 3tan a) / (2cot a + tan a)`

`<=>` `E = (tana.cot a+ 3tan a.tana) / (2cot a.tana + tan a.tana)`

`<=>` `E = (1+ 3tan^2a) / (2.1 + tan^2a)`

`<=>` `E = (1+ 3tan^2a) / (2 + tan^2a)`

`<=>` `E = (1+ tan^2a + 2 tan^2a + 2 - 2) / (1 + 1 + tan^2a)`

`<=>` `E = ((1+ tan^2a )+ (2 tan^2a + 2) - 2) / (1 + (1 + tan^2a))`

`<=>` `E = ((1+ tan^2a )+ 2( tan^2a +1 ) - 2) / (1 + (1 + tan^2a))`

`<=>` $E = \dfrac{\dfrac{1}{cos^2a} + 2\dfrac{1}{cos^2a} -2}{1 + \dfrac{1}{cos^2a}}$

`<=>` $E = \dfrac{\dfrac{1}{(\dfrac{-2}{3})^2} + 2\dfrac{1}{(\dfrac{-2}{3})^2} -2}{1 + \dfrac{1}{(\dfrac{-2}{3})^2}}$

`<=>` $E = \dfrac{\dfrac{1}{\dfrac{4}{9}} + 2\dfrac{1}{\dfrac{4}{9}} -2}{1 + \dfrac{1}{\dfrac{4}{9}}}$

`<=>` $E = \dfrac{\dfrac{9}{4} + \dfrac{9}{2} -2}{1 +\dfrac{9}{4}}$

`<=>` $E = \dfrac{\dfrac{19}{4}}{\dfrac{13}{4}}$

`<=>` `E = 19/13`

Vậy `E = 19/13` khi `cos a = -2/3`