Algebraic and geometric in inverse kinematic

I'm just wondering that is there any case that when algebraic way can't solve the problem while the geometric can ? Cause I'm working on a 2DOF robotics arm This one, I know the length of L1 and L2, location that I want for the end effector, then I tried calculating the angles by using algebraic but it gave me cos(alpha) > 1, but when I tried solving with geometric, I can find the solution, so is it because I use a wrong way in algebraic ?
Thank you very much.