When you do something `without breaking a sweat’, you do it without any difficulty. You find the task so easy that you don’t have to exert yourself at all; you perform the task very easily or quickly. There is no need for you to sweat.
Example: Rahul answered all the questions without breaking a sweat.
Another expression that has more or less the same meaning is `no sweat’.
Example: “Listen, I’ll carry the two large suitcases. No sweat at all”.
When you `break into a sweat’, you actually start sweating. And when is it that we begin to sweat? When we exert ourselves or when we are extremely nervous or frightened about something.
Examples: The children broke into a sweat when they heard strange noises coming from the bedroom. * Uma broke into a sweat when she saw the policeman walking towards her.