Đáp án:
\(\left[ \begin{array}{l}
\sin x = \dfrac{3}{{\sqrt {10} }}\\
\sin x = - \dfrac{3}{{\sqrt {10} }}
\end{array} \right. \to \left[ \begin{array}{l}
\cos x = \dfrac{1}{{\sqrt {10} }}\\
\cos x = - \dfrac{1}{{\sqrt {10} }}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
\cot x = \dfrac{1}{3}\\
\to \cos x = \dfrac{1}{3}\sin x\\
{\sin ^2}x + {\cos ^2}x = 1\\
\to \dfrac{1}{9}{\sin ^2}x + {\sin ^2}x = 1\\
\to \dfrac{{10}}{9}{\sin ^2}x = 1\\
\to {\sin ^2}x = \dfrac{9}{{10}}\\
\to \left[ \begin{array}{l}
\sin x = \dfrac{3}{{\sqrt {10} }}\\
\sin x = - \dfrac{3}{{\sqrt {10} }}
\end{array} \right. \to \left[ \begin{array}{l}
\cos x = \dfrac{1}{{\sqrt {10} }}\\
\cos x = - \dfrac{1}{{\sqrt {10} }}
\end{array} \right.\\
\to \tan x = 3
\end{array}\)
