Đáp án:
\(\left[ \begin{array}{l}
\sin x = \dfrac{1}{{\sqrt {37} }}\\
\sin x = - \dfrac{1}{{\sqrt {37} }}
\end{array} \right. \to \left[ \begin{array}{l}
\cos x = \dfrac{6}{{\sqrt {37} }}\\
\cos x = - \dfrac{6}{{\sqrt {37} }}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
\cot x = 6\\
\to \tan x = \dfrac{1}{6}\\
\to \dfrac{{\cos x}}{{\sin x}} = 6\\
\to \cos x = 6\sin x\\
{\sin ^2}x + {\cos ^2}x = 1\\
\to {\sin ^2}x + 36{\sin ^2}x = 1\\
\to 37{\sin ^2}x = 1\\
\to {\sin ^2}x = \dfrac{1}{{37}}\\
\to \left[ \begin{array}{l}
\sin x = \dfrac{1}{{\sqrt {37} }}\\
\sin x = - \dfrac{1}{{\sqrt {37} }}
\end{array} \right. \to \left[ \begin{array}{l}
\cos x = \dfrac{6}{{\sqrt {37} }}\\
\cos x = - \dfrac{6}{{\sqrt {37} }}
\end{array} \right.
\end{array}\)
