Question

The period of ${\cot h}\left( \frac{nx}{4} \right)$ is.

• A. $\frac{\pi i}{n}$
• B. $\frac{4\pi i}{n}$
• C. $\frac{n\pi i}{4}$
• D. $\pi i$

Answer 1

Answer: (B)

$\frac{4\pi i}{n}$

Answer 2

$\coth\left( \frac{nx}{4} \right) = \coth\left( \pi i + \frac{nx}{4} \right) = {\cot h}\frac{n}{4}\left( \frac{4\pi i}{n} + x \right)$

∴ Period is $\frac{4\pi i}{n}$.