Arcsine as Integral/Lemma 1

Proof
For this proof only, let $\sin_A$ be the analytic sine function from Definition:Sine/Complex Numbers.

Consider $\int_{0}^{x}\frac{1}{\sqrt{1-x^2} }\d{x}$

Let $x=\sin_A\left(\Theta\right)\iff x=\arcsin_A\left(\Theta\right)$