let $f:\mathbb{C}\rightarrow\mathbb{C}, f(z)=\cos(z)$. I am looking for a biholomorphic function $\varphi:U\rightarrow V$ with $U,V$ neighbourhoods of $0$ so that $f(z)=f(0)+(\varphi(z))^2$ for all $z\in U$.
I have tried to work with the Taylorseries but that didn't help. I also have no idea how to choose $U$ and $V$.
Thanks for you help.