An 'azimah is the ordinary governing rule. A rukhsah is an authorized concession for a recognized excuse. Its forms differ: the original restriction may remain while a concession is granted, or the legal assessment may change under the excuse.
Coercion to utter words of disbelief while retaining faith in the heart presents a different legal problem from some necessity-based food and drink concessions. The life of an innocent third party cannot simply be taken because one's own life is threatened.
Method of application: establish the excuse, the original duty or prohibition, the type of concession and its conditions.
Not every hardship creates a concession, and not every permitted concession is equally recommended to take.