Question

How to evaluate cot 3pi/2

Answer 1

`\huge\boxed{\cot(3\pi)/(2)=0}`

Explanation:

`\text{We know}\ \cot x=\cot(x\pm\pi)\ \text{and}\ \cot(-x)=-\cot x.\\\\\text{We have}\ \cot(3\pi)/(2)=\cot(\pi+2\pi)/(2)=\cot\bigg((\pi)/(2)+(2\pi)/(2)\bigg)=\cot\bigg((\pi)/(2)+\pi\bigg)=\cot(\pi)/(2)\\\\\cot\bigg((\pi)/(2)\bigg)=0\\\\\text{Therefore}\ \cot(3\pi)/(2)=0.`