Đáp án:
\(\tan x = - \dfrac{1}{2}\)
Giải thích các bước giải:
\(\begin{array}{l}
Do:x \in \left( { - \dfrac{\pi }{2};0} \right)\\
\to \left\{ \begin{array}{l}
\cos x > 0\\
\sin x < 0
\end{array} \right.\\
\cot x = - 2\\
\to \dfrac{{\cos x}}{{\sin x}} = - 2 \to \cos x = - 2\sin x\\
Có:{\sin ^2}x + {\cos ^2}x = 1\\
\to 4{\sin ^2}x + {\sin ^2}x = 1\\
\to {\sin ^2}x = \dfrac{1}{5}\\
\to \sin x = - \dfrac{1}{{\sqrt 5 }}\\
\to \cos x = \dfrac{2}{{\sqrt 5 }}\\
\to \tan x = - \dfrac{1}{{\sqrt 5 }}:\dfrac{2}{{\sqrt 5 }} = - \dfrac{1}{2}
\end{array}\)
