I tried to draw the situation. One adds two forces via the parallelogram rule or via the chain rule. The "longer" diagonale is the resultant force in both case. So the sign before the cosinus function depends on whether the vectors start from one point (2) or they follow each other (1).
Thank you Dr. Éva Szőke for your answer, but I think when we assume that there are two collinear forces in the same direction (angle between them equal to zero) or in the opposite direction (angle between them 180), the second equation is suitable to calculate the resultant force.
Yes. It depends on that how one defines the angle between two vectors. Usually one places both vectors in a common starting point but one could find out another kind of definition.