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I have two points in the sky and I have their coordinates in Azimuth and Elevation angles with respect to position O. I want to find the scalar angle between the two points w.r.t. position O. Thank you so much for your help!

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The simplest is to convert from spherical to Cartesian coordinates and take the dot product (cosine of the angle).

https://en.wikipedia.org/wiki/Spherical_coordinate_system#Cartesian_coordinates

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