\(\tan \alpha = {{\sin \alpha } \over {\cos \alpha }},\cot \alpha = {{{\rm{cos}}\alpha } \over {\sin \alpha }}\)
Suy ra \(\tan (\alpha + k\pi ) = {{\sin (\alpha + k\pi )} \over {\cos (\alpha + k\pi )}}\)
+) Nếu \(k\) chẵn ta có:
\(\sin(α+kπ) = \sin α\)
\(\cos(α+kπ) = \cos α\)
+) Nếu \(k\) lẻ ta có:
\(\sin(α+kπ) = - \sin α\)
\(\cos(α+kπ) = - \cos α\)
Suy ra \(\tan(α+kπ) = \tanα ; \, k ∈\mathbb Z.\)
Tương tự ta có: \(\cot(α+kπ) = \cotα;\, k ∈\mathbb Z.\)
