Note: This post is just some notes for a discussion.
We can start by writing it simply as
Now we use and assume . After expanding the expression using the coordinates,
we have to find now a way to get rid of the square roots. Taking as a common factor,
As we know the argument of the square root is very close to 1, we can use a first order approximation, :
Replacing in the original expression,
we get expressions matching the ones in the slides apart from some amplitude and phase conventions.