Đáp án:
\[C = \dfrac{{ - 3}}{2}\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\tan x = - 2 \Leftrightarrow \dfrac{{\sin x}}{{\cos x}} = - 2 \Leftrightarrow \sin x = - 2\cos x\\
{\sin ^2}x + {\cos ^2}x = 1\\
\Leftrightarrow {\left( { - 2\cos x} \right)^2} + {\cos ^2}x = 1\\
\Leftrightarrow {\cos ^2}x = \dfrac{1}{5}\\
C = \dfrac{{\sin x + 5\cos x}}{{{{\sin }^3}x - 2{{\cos }^3}x}} = \dfrac{{\left( { - 2\cos x} \right) + 5\cos x}}{{{{\left( { - 2\cos x} \right)}^3} - 2{{\cos }^3}x}} = \dfrac{{3\cos x}}{{ - 10{{\cos }^3}x}} = \dfrac{{ - 3}}{{10{{\cos }^2}x}} = \dfrac{{ - 3}}{{10.\dfrac{1}{5}}} = - \dfrac{3}{2}
\end{array}\)
