$$ \cot\alpha = \frac{b}{a} $$
$$ \cot\beta = \frac{a}{b} $$
$$
\begin{aligned}
& \tan\alpha \cdot \cot\alpha = 1 \ \Rightarrow \\ \\
& \tan\alpha = \frac{1}{\cot\alpha}
\end{aligned}
$$
$$
\begin{aligned}
& \cot\alpha = \frac{\cos\alpha}{\sin\alpha} \\ \\
& \tan\alpha = \frac{\sin\alpha}{\cos\alpha}
\end{aligned}
$$
$$
\begin{aligned}
& \tan(\alpha + \beta) = \frac{\tan\alpha + \tan\beta}{1 - \tan\alpha\tan\beta} \\ \\
& \tan(\alpha - \beta) = \frac{\tan\alpha - \tan\beta}{1 + \tan\alpha\tan\beta}
\end{aligned}
$$
$$
\begin{aligned}
& \tan 2\alpha = \frac{2\cdot\tan\alpha}{1 - {\tan}^2\alpha} \\ \\
& \left|\tan\frac{\alpha}{2}\right| = \sqrt{\frac{1-\cos\alpha}{1+\cos\alpha}} \\ \\
& \tan(-\alpha) = -\tan\alpha \\ \\
& \cot(-\alpha) = -\cot\alpha
\end{aligned}
$$
