Answer
The function is odd. Notice that the function is symmetric with respect to the origin.
$f(-x)=-f(x)$, that is $(-x)^2cot(-x)=-x^2cot~x$
Work Step by Step
$f(x)=x^2cot~x$
$f(-x)=(-x)^2cot(-x)=x^2\frac{cos(-x)}{sin(-x)}=x^2\frac{cos~x}{-sin~x}=-x^2\frac{cos~x}{sin~x}=-x^2cot~x=-f(x)$
