The vectors OA, OB and OC are:

OA = (0, 0, 1) OB = (cosu, 0, sinu) OC = (0, cosv, sinv).

Since these are unit vectors, the angles between the vectors, and hence the lengths of the sides of triangle ABC, are:

a =cos-1OB.OC = cos-1sinu sinv b = cos-1OA.OC = cos-1sinv c = cos-1OB.OA = cos-1sinu.

Hence

cosa = cosb cosc.