Using the fact that $f(x) = g(x)$ on $I = ]-\pi/2, \pi/2[$ where $f(x) = \frac{\sin x + 1}{\cos x}$ and $g$ is the sum of the power series $\sum_{n \in \mathbb{N}} \frac{\alpha_n}{n!} x^n$, deduce that $R = \pi/2$.
Using the fact that $f(x) = g(x)$ on $I = ]-\pi/2, \pi/2[$ where $f(x) = \frac{\sin x + 1}{\cos x}$ and $g$ is the sum of the power series $\sum_{n \in \mathbb{N}} \frac{\alpha_n}{n!} x^n$, deduce that $R = \pi/2$.