Đáp án:
\(\left[ \begin{array}{l}
\cos a = \dfrac{1}{{\sqrt 5 }}\\
\cos a = - \dfrac{1}{{\sqrt 5 }}
\end{array} \right. \to \left[ \begin{array}{l}
\sin a = \dfrac{2}{{\sqrt 5 }}\\
\sin a = - \dfrac{2}{{\sqrt 5 }}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
\tan a = 2\\
\to \sin a = 2\cos a\\
{\sin ^2}a + {\cos ^2}a = 1\\
\to 4{\cos ^2}a + {\cos ^2}a = 1\\
\to {\cos ^2}a = \dfrac{1}{5}\\
\to \left[ \begin{array}{l}
\cos a = \dfrac{1}{{\sqrt 5 }}\\
\cos a = - \dfrac{1}{{\sqrt 5 }}
\end{array} \right. \to \left[ \begin{array}{l}
\sin a = \dfrac{2}{{\sqrt 5 }}\\
\sin a = - \dfrac{2}{{\sqrt 5 }}
\end{array} \right.\\
\to \cot a = \dfrac{1}{2}
\end{array}\)
