Answer
The function is even. Notice that the function is symmetric with respect to the y-axis.
$f(-x)=f(x)$, that is $(-x)csc(-x)=x~csc~x$
Work Step by Step
$f(x)=x~csc~x$
$f(-x)=(-x)csc(-x)=-x\frac{1}{sin(-x)}=-x\frac{1}{-sin~x}=x\frac{1}{sin~x}=x~csc~x=f(x)$
