Đáp án:
\(\left[ \begin{array}{l}
\cos a = \dfrac{2}{{\sqrt 5 }}\\
\cos a = - \dfrac{2}{{\sqrt 5 }}\\
\cos a = \dfrac{1}{{\sqrt 5 }}\\
\cos a = - \dfrac{1}{{\sqrt 5 }}
\end{array} \right. \to \left[ \begin{array}{l}
\sin a = \dfrac{1}{{\sqrt 5 }}\\
\sin a = - \dfrac{1}{{\sqrt 5 }}\\
\sin a = \dfrac{2}{{\sqrt 5 }}\\
\sin a = - \dfrac{2}{{\sqrt 5 }}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
Do:\sin a.\cos a = \dfrac{2}{5}\\
\to \sin a = \dfrac{2}{{5.\cos a}}\left( {DK:\cos a \ne 0} \right)\\
Có:{\sin ^2}a + {\cos ^2}a = 1\\
\to \dfrac{4}{{25{{\cos }^2}a}} + {\cos ^2}a = 1\\
\to 25{\cos ^4}a - 25{\cos ^2}a + 4 = 0\\
\to \left[ \begin{array}{l}
{\cos ^2}a = \dfrac{4}{5}\\
{\cos ^2}a = \dfrac{1}{5}
\end{array} \right.\\
\to \left[ \begin{array}{l}
\cos a = \dfrac{2}{{\sqrt 5 }}\\
\cos a = - \dfrac{2}{{\sqrt 5 }}\\
\cos a = \dfrac{1}{{\sqrt 5 }}\\
\cos a = - \dfrac{1}{{\sqrt 5 }}
\end{array} \right. \to \left[ \begin{array}{l}
\sin a = \dfrac{1}{{\sqrt 5 }}\\
\sin a = - \dfrac{1}{{\sqrt 5 }}\\
\sin a = \dfrac{2}{{\sqrt 5 }}\\
\sin a = - \dfrac{2}{{\sqrt 5 }}
\end{array} \right.\\
\to \left[ \begin{array}{l}
\tan a = \dfrac{1}{2}\\
\tan a = 2
\end{array} \right. \to \left[ \begin{array}{l}
\cot a = 2\\
\cot a = \dfrac{1}{2}
\end{array} \right.
\end{array}\)
