I'm trying to undestand how a book derives somes physical constants, but I'm struggling with this aproximation: it goes from $\dfrac{1}{\sqrt{(1 - i \tan(x))}}$ to $(1 + i\dfrac{\tan(x)}{2})$, where $i$ is the imaginary unit. It is also mentioned that $\tan(x)$ is close to $0$ so it can aproximated in this way. Any tips?
2026-04-29 00:53:11.1777423991
Can you help me to understand this aproximation?
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It uses the limit development of $(1+x)^c$, where $c=-{1\over 2}$.
https://en.wikipedia.org/wiki/Binomial_series