( 2 A ) ( 1 + A )1 + A + A is equal to:

Answer: Option B

In these type of questions we can go through option-
From option B
$$\begin{array}{rl}& \frac{\left(2\sin A\right)\left(1+\sin A\right)}{\left(1+\sin A\right)+\cos A}=1-\cos A+\sin A\\ & 2\sin A\left(1+\sin A\right)={\left(1+\sin A\right)}^2-{\cos }^{2}A\\ & 2\sin A\left(1+\sin A\right)=1+\sin 2A+2\sin A-1+{\sin }^{2}A\\ & 2\sin A\left(1+\sin A\right)=2\sin A\left(1+\sin A\right)\\ & \text{L}\text{.H}\text{.S}\text{.}=\text{R}\text{.H}\text{.S}\text{.}\\ & \\ & \mathbf{Alternate}:\\ & \text{Put }A=90^{\circ }\\ & \frac{\left(2\sin {90}^{\circ }\right)\left(1+\sin {90}^{\circ }\right)}{1+\sin {90}^{\circ }+\cos {90}^{\circ }}=2\\ & \text{Now from option B}\\ & 1+\sin A-\cos A\\ & =1+\sin 90^{\circ }-\cos 90^{\circ }\\ & =1+1-0\\ & =2\end{array}$$