Filter by maximum distance from latitude and longitude

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I have three variables: latitude, longitude and distance. I want to calculate the latitude and longitude ranges where the distance is less than the given distance.

Basing on this answer I'm guessing that

$$ D_{ab} > R \cos^{-1} ( \cos \theta_a \cos \theta_b \cos(\phi_b - \phi_a) + \sin \theta_a \sin \theta_b) $$

Is it right? Could it be simplified?