Đáp án:
\[D = - \dfrac{{11}}{5}\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\cos x = - \dfrac{2}{5} \Rightarrow {\cos ^2}x = \dfrac{4}{{25}}\\
{\sin ^2}x = 1 - {\cos ^2}x = 1 - {\left( { - \dfrac{2}{5}} \right)^2} = \dfrac{{21}}{{25}}\\
D = \dfrac{{2\cot x - 3\tan x}}{{\cot x + \tan x}}\\
= \dfrac{{2\dfrac{{\cos x}}{{\sin x}} - 3\dfrac{{\sin x}}{{\cos x}}}}{{\dfrac{{\cos x}}{{\sin x}} + \dfrac{{\sin x}}{{\cos x}}}}\\
= \dfrac{{\dfrac{{2{{\cos }^2}x - 3{{\sin }^2}x}}{{\sin x.\cos x}}}}{{\dfrac{{{{\cos }^2}x + {{\sin }^2}x}}{{\sin x.\cos x}}}}\\
= \dfrac{{2{{\cos }^2}x - 3{{\sin }^2}x}}{{{{\sin }^2}x + {{\cos }^2}x}}\\
= 2{\cos ^2}x - 3{\sin ^2}x\,\,\,\,\,\,\,\,\,\,\left( {{{\sin }^2}x + {{\cos }^2}x = 1} \right)\\
= 2.\dfrac{4}{{25}} - 3.\dfrac{{21}}{{25}}\\
= - \dfrac{{11}}{5}
\end{array}\)
