Comment with a drawing, illustrating points made by previous comments:
Green is current orbit
Red is the new, desired orbit
Orange orbit has the same inclination as the desired orbit, but higher apogee
"a" is desired inclination change
"b" is optimum thrust direction
Blue vector is the thrust vector to achieve red orbit inclination "a" without affecting scalar velocity or apoapsis
Purple vector is the thrust vector at right angle to the green orbit needed to achieve desired new orbital inclination "a". However, it also changes scalar velocity so it will raise apoapsis above that for the red orbit. Higher orbit from purple thrust is illustrated in orange.
Since Red-Blue-Green is an isosceles triangle, b=1/2(180*-a)
This description assumes the usual disclaimer used for Hohmann transfers: the thrust is applied as an instantaneous impulse. In reality, the thrust duration for a large inclination change would be a significant portion of the launch burn and occupy a significant orbital phase angle. This would necessitate changing thrust angle and graded (not instantaneous) course changes. Rocket science, in other words.