To master C programming language is necessary to have a full knowledge
of the standard library?
No, it's not necessary, but you're going to.
Suppose that is an extra-time cost to learn.
This isn't a very good approach to learning. You are treating your time like a precious resource and you're trying to allocate it sparingly, learning only what has the biggest bang for the buck, and skipping everything else. Frankly, I don't think there are any shortcuts. If you never charge full-speed into a Turing tar-pit, or butt heads against type-casting, or lose your way with pointer confusion, then I don't think you can "master" such things. I think doing stupid things and learning some cruft is an essential part of learning. If you don't fall into those traps now, you're just setting yourself up for a larger fall later. Go tackle stdlib with a voracious appetite. You have to approach new code with new functions not as something to try and side-step, but as opportunity to expand your repertoire.
In short, learn as if you were going to live forever.