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