My physics textbook does the approximation that $$r=\frac{r_0}{1-\frac{A}{r_0}\sin\theta}\approx r_0\left( 1+\frac A r_0\sin\theta\right)$$ when ##A/r_0 \ll 1##. Can someone please explain how it is done?
For what it's worth, basically every approximation you see like this in physics comes from the Taylor series of a function. The fact that you see an ##\frac{A}{r_0}\sin(\theta)## suggests that is what's being plugged into the function.