Characterize an analytic function with restriction of its growth
Characterize all analytic functions $f(x)$ in $|z|<1$ such that $|f(z)|\leq|\sin(1/z)|$ for all points in punctured disk.
I think we should change the form of $\sin(1/z)$ to find a connection with polynomial which $f(x)$ can be expanded into. But I don't know how to do that.
**Hint:**
Take the sequence $\\{z_n\\}=\left\\{\frac{1}{n\pi}\right\\}$ and use **Identity theorem**.