Answer
A function is odd function if f(-x)=-f(x).
$cot\theta=\frac{cos\theta}{sin\theta}$
$cot(-\theta)=\frac{cos(-\theta)}{sin(-\theta)}$
=$\frac{cos(\theta)}{-sin\theta}$ [ because $cos(-\theta)=cos(\theta)$]
=$-cot\theta$
Hence, $cot(-\theta)=-cot\theta$
So, cotangent is an odd function.
Work Step by Step
A function is odd function if f(-x)=-f(x).
$cot\theta=\frac{cos\theta}{sin\theta}$
$cot(-\theta)=\frac{cos(-\theta)}{sin(-\theta)}$
=$\frac{cos(\theta)}{-sin\theta}$ [ because $cos(-\theta)=cos(\theta)$]
=$-cot\theta$
Hence, $cot(-\theta)=-cot\theta$
So, cotangent is an odd function.