Calculus (3rd Edition)

Both $\tan θ$ and $\cot θ$ are periodic with period $\pi$.
Since \begin{aligned} &\tan (\theta+\pi)=\frac{\sin (\theta+\pi)}{\cos (\theta+\pi)}=\frac{-\sin \theta}{-\cos \theta}=\tan \theta\\ &\cot (\theta+\pi)=\frac{\cos (\theta+\pi)}{\sin (\theta+\pi)}=\frac{-\cos \theta}{-\sin \theta}=\cot \theta \end{aligned} Then both $\tan θ$ and $\cot θ$ are periodic with period $\pi$.