If sin(A + B) = cos(A + B), what is the value of tanA?

$$\eqalign{ & \sin \left( {A + B} \right) = \cos \left( {A + B} \right) \cr & \frac{{\sin \left( {A + B} \right)}}{{\cos \left( {A + B} \right)}} = 1 \cr & \tan \left( {A + B} \right) = 1 \cr & \tan \left( {A + B} \right) = \tan {45^ \circ } \cr & A + B = {45^ \circ } \cr & A = {45^ \circ } - B \cr & \tan A = \tan {45^ \circ } - \tan B \cr & \tan A = \frac{{\tan {{45}^ \circ } - \tan B}}{{1 + \tan {{45}^ \circ }\tan B}} \cr & \tan A = \frac{{1 - \tan B}}{{1 + \tan B}} \cr} $$