Given values for cos(A+B) and B, there are two possible values for cos(A). You're on the right track, all you need is to recognize that the arccosine of a number may be either positive or negative:

For example if B=60 degrees and cos(A+B) = 0.5, possible values for cos(A) are 1 and -0.5. In other words values for A of 0 and 240 degrees are both valid.