$$\cot(\alpha-\beta)=\frac{cot\alpha.cot\beta+1}{cot\beta-cot\alpha}$$
$\alpha \notin \pi n_{2},\pi n_{2}+\beta $
$\forall n_{2}\in \mathrm{Z}$
$\nexists n_{1}\in \mathrm{Z}\text{ : }\beta =\pi n_{1}$
$\beta \notin \pi n_{2},\pi n_{2}+\alpha $
$\forall n_{2}\in \mathrm{Z}$
$\nexists n_{1}\in \mathrm{Z}\text{ : }\alpha =\pi n_{1}$
