Đáp án:
$\begin{array}{l}
Do:{\sin ^2}a + {\cos ^2}a = 1\\
\tan a = \dfrac{{\sin a}}{{\cos a}} = \dfrac{1}{{\cot a}}\\
a)\cos a = 0,8\\
\Leftrightarrow {\sin ^2}a = 1 - 0,{8^2} = \dfrac{9}{{25}}\\
\Leftrightarrow \sin a = \pm 0,6\\
\Leftrightarrow \left\{ \begin{array}{l}
\tan a = \pm \dfrac{{0,6}}{{0,8}} = \dfrac{3}{4}\\
\cot a = \pm \dfrac{4}{3}
\end{array} \right.\\
b)\tan a = 2\\
\Leftrightarrow \cot a = \dfrac{1}{2}\\
\dfrac{1}{{{{\cos }^2}a}} = {\tan ^2}a + 1 = 5\\
\Leftrightarrow {\cos ^2}a = \dfrac{1}{5}\\
\Leftrightarrow {\sin ^2}a = 1 - \dfrac{1}{5} = \dfrac{4}{5}\\
\Leftrightarrow \cos a = \pm \dfrac{{\sqrt 5 }}{5};\sin a = \pm \dfrac{{2\sqrt 5 }}{5}
\end{array}$
