What eats a a bald eagle and a cougar?

Answer 1

Something like this would be pretty rare. A Bald Eagle may eat smaller owls such as screech owls, but probably not a Great Horned. An eagle may kill a Great Horned in a chance encounter, perhaps over a nest site.

Answer 2

Very, very rarely. But if an eagle where to land in front of a hungry cougar it might have a go at catching it.

Answer 3

Only when the cougar has died. Cougars, especially adults, can easily kill eagles.