Đáp án:
$\begin{array}{l}
Dkxd:\left\{ \begin{array}{l}
\sin a\# 0\\
\cos a\# 0
\end{array} \right. \Leftrightarrow x\# \dfrac{{k\pi }}{2}\\
a)\tan a - \cot a = \dfrac{7}{2}\\
\Leftrightarrow \tan a - \dfrac{1}{{\tan a}} = \dfrac{7}{2}\\
\Leftrightarrow {\tan ^2}a - \dfrac{7}{2}\tan a - 1 = 0\\
\Leftrightarrow 2{\tan ^2}a - 7\tan a - 2 = 0\\
\Leftrightarrow \tan a = \dfrac{{7 \pm \sqrt {65} }}{4}\\
\Leftrightarrow \cot a = \dfrac{1}{{\tan a}} = \dfrac{{ - 7 \pm \sqrt {65} }}{4}\\
Vậy\,\tan a = \dfrac{{7 \pm \sqrt {65} }}{4};\cot a = \dfrac{{ - 7 \pm \sqrt {65} }}{4}\\
b)\tan a + \cot a = 2\\
\Leftrightarrow \tan a + \dfrac{1}{{\tan a}} = 2\\
\Leftrightarrow {\tan ^2}a - 2\tan a + 1 = 0\\
\Leftrightarrow {\left( {\tan a - 1} \right)^2} = 0\\
\Leftrightarrow \tan a = 1\\
\Leftrightarrow \cot a = 1\\
Vậy\,\tan a = \cot a = 1
\end{array}$
