What is the value of $$\frac{{\sin \left( {A + B} \right)}}{{\sin A\cos B}}?$$

A. 1 + cotAtanB

B. 1 + tanAcotB

C. 1 - sinAcosB

D. 1 - cotAtanB

Answer: Option A

Solution(By Examveda Team)

$$\eqalign{ & \frac{{\sin \left( {A + B} \right)}}{{\sin A.\cos B}} \cr & = \frac{{\sin A.\cos B + \cos A.\sin B}}{{\sin A.\cos B}} \cr & = 1 + \frac{{\cos A.\sin B}}{{\sin A.\cos B}} \cr & = 1 + \cot A.\tan B \cr} $$