What is the value of ( A + B ) A B?

Answer: Option A

$$\begin{array}{rl}& \frac{\sin \left(A+B\right)}{\sin A.\cos B}\\ & =\frac{\sin A.\cos B+\cos A.\sin B}{\sin A.\cos B}\\ & =1+\frac{\cos A.\sin B}{\sin A.\cos B}\\ & =1+\cot A.\tan B\end{array}$$