Consider the function $f(z) = Sin\left(\frac{1}{cos(1/z)}\right)$, the point $z = 0$
a removale singularity
a pole
an essesntial singularity
a non isolated singularity
Since $Cos(\frac{1}{z})$ = $1- \frac{1}{2z^2}+\frac{1}{4!z^4} - ..........$ $$ = (1-y), where\ \ y=\frac{1}{2z^2}+\frac{1}{4!z^4} - ..........$$
Thus $Sin\left(\frac{1}{1-y}\right) = Sin(1+y+y^2 +y^3+.......)$ = $\sum_{-\infty} ^{\infty}$$ a_n z^n$, thus $z=0$ is an issolated singularity.
Please check my solution is right or not. Also I want to know that how to check an non- isolated singularity