Take a look at my answer to a related question http://gis.stackexchange.com/questions/142136/proof-of-part-of-haversine-formula

The first part is directly relevant:

The radius, r, of the small circle joining all points at latitude, φ is

r = R cos φ

where R is the radius of the sphere.

However, instead of the *chord* length of a straight line joining two points on the same latitude (a requirement of that question), you want the simpler *arc* length of part of the small circle. It is simply

AD = r sin dλ

where dλ is the difference in longitude of A and D.

As always in spherical trigonometry, things get more complicated in the case of an ellipsoid. The first equation above relates only to the globe being a simple sphere.