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