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