At z = 0, the function 1/(z-sinz ) of a complex variable z has

Correct option is D

Concept:
A pole of an analytic function is a point at which the function goes to infinity. It is also known as the singularity of the function.

For example, if the function is given as : f(x)=1/x−2.  At x = 2, the function will become infinite. So,  x = 2  is the singularity point of the function or the pole of the function.
Solution:
The sine function can be written as :

Substituting the above equation in the function:

Now, this function will become infinity at point  z=0. 
But the power of  z is  3, which states the order of the pole.