As a new poster to this forum (but not a new player to Risk) I am unsure if this tactic has ever been discussed before. I have used this many times agaisnt players with big egos and it has worked for most of them.
The tatic is very similar to a pincer move or "The Horns of the Bull" which is what the Zulus called it when they fought agaisnt the British. The basics are very easy to understand, and anyone should be able to pull it off. However it takes practics to execute the move perfectly.
If your friend has a big ego, by all means let him keep it. Show weakness. If your "empire" borders his show him weakness by creating a weak border with his. If your friend is so cocky, he won't be able to resist the chance to strike at you and will plow through your so called "weak" front.
The point is to cause him to overextend himself, by plunging into your empire especially your "weak" one you have hopefully done two things. First you have caused him to forget about advancing in other areas on the board, and second you have shown to other players how strong your cocky friend will be if he manages to eliminate you.
When it is your turn to retaliate, cut off his forces. Encircle his invading force and reclaim the bits and peices of your empire. If all has worked according to plan, you have cut off his invading force from the rest of his forces and have now placed a strong border between his empire and his invading force.
You can now eliminate his invading force and crush his valuable troops, while the other players hopefully now strike at your cocky friend. You have enclosed his force with the "horns" and now he has to face the bull. If all works well you can eliminate his "invasion force" while he cannot do anything about it, as he must defend himself on the fronts he forgot about.
It has worked in the past for me, and I hope it shall work for you. Good luck.