For the function :
$$f(z)= \sin\bigg(\frac{1}{\cos(\frac1z)}\bigg)$$
the point $z=0$ is:
1)a removable singularity
2)a pole
3)an essential singularity
4)a non-isolated singularity
The answer seems to be 3)an essential singularity.
But I arrived at 1)removable singularity because when $f(z)$ has removable singularity,
$\lim\limits_{z\to0}$ $(z-z_0)$$f(z)=0$. (Since $\lim\limits_{x\to a}$$f(x)=f(a)$.)
Can someone help me, pointing out where I had gone wrong? Thanks in advance.