Đáp án:
\(\left[ \begin{array}{l}
\cot a = \dfrac{1}{{2\sqrt 6 }}\\
\cot a = - \dfrac{1}{{2\sqrt 6 }}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
Do:\cos a = \dfrac{1}{5}\\
{\sin ^2}a + {\cos ^2}a = 1\\
\to {\sin ^2}a + \dfrac{1}{{25}} = 1\\
\to {\sin ^2}a = \dfrac{{24}}{{25}}\\
\to \left[ \begin{array}{l}
\sin a = \dfrac{{2\sqrt 6 }}{5}\\
\sin a = - \dfrac{{2\sqrt 6 }}{5}
\end{array} \right.\\
\to \left[ \begin{array}{l}
\tan a = \dfrac{{\sin a}}{{\cos a}} = 2\sqrt 6 \\
\tan a = - 2\sqrt 6
\end{array} \right.\\
\to \left[ \begin{array}{l}
\cot a = \dfrac{1}{{\tan a}} = \dfrac{1}{{2\sqrt 6 }}\\
\cot a = - \dfrac{1}{{2\sqrt 6 }}
\end{array} \right.
\end{array}\)
