For small distances, you can use:
tan course = (Dlong x cos Mean Lat) / Dlat
distance = d'lat / cos course
For larger distances, you would require a table of Meridional Parts, (parts of the meridian in Mercator's projection, corresponding to each minute of latitude from the equator up to 70 or 80 degrees; tabulated numbers representing these parts used in projecting charts, and in solving cases in Mercator's sailing). Then the calculation would be tan course = dlong / difference in meridional parts.
Then for great circle, you simply move into the spherical trig.