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

Answer: Option A

$$\begin{array}{rl}& \sin \left(A+B\right)=\cos \left(A+B\right)\\ & \frac{\sin \left(A+B\right)}{\cos \left(A+B\right)}=1\\ & \tan \left(A+B\right)=1\\ & \tan \left(A+B\right)=\tan 45^{\circ }\\ & A+B=45^{\circ }\\ & A=45^{\circ }-B\\ & \tan A=\tan 45^{\circ }-\tan B\\ & \tan A=\frac{\tan {45}^{\circ }-\tan B}{1+\tan {45}^{\circ }\tan B}\\ & \tan A=\frac{1-\tan B}{1+\tan B}\end{array}$$