# A question related to uniqueness principle theorem.

We know that the equation $\sin^2z+ \cos^2z=1$ which holds $\forall z \in\Bbb R$, also holds $\forall z \in\Bbb C$.

This is obvious under the shadow of following theorem:

Uniqueness principle theorem :If $f$ and $g$ are analytic functions on a domain $D$, and if $f(z)=g(z)$ for $z$ belonging to a set that has a non isolated point, then $f(z)=g(z)$ for all $z\in D$.