What is the value of 1 + ^2A1 + A?

Answer: Option C

$$\begin{array}{rl}& 1+\frac{{\tan }^{2}A}{1+\sec A}\\ & =1+\frac{{\sec }^{2}A-1}{1+\sec A}\\ & =\frac{1+\sec A+{\sec }^{2}A-1}{1+\sec A}\\ & =\frac{\sec A\left(1+\sec A\right)}{1+\sec A}\\ & =\sec A\end{array}$$