1 + sin 1 - sin + 1 - sin 1 + sin is equal to?

Answer: Option D

$$\begin{array}{rl}& \sqrt{\frac{1+\text{sin }\theta }{1-\text{sin }\theta }}\text{ + }\sqrt{\frac{1-\text{sin }\theta }{1+\text{sin }\theta }}\\ & =\frac{{\left(\sqrt{1+\text{sin }\theta }\right)}^2+{\left(\sqrt{1-\text{sin }\theta }\right)}^2}{\sqrt{1-{\sin }^2\theta }}\\ & =\frac{1+\text{sin }\theta +\text{1}-\text{sin }\theta }{\text{cos}\theta }\\ & =\frac{2}{\text{cos}\theta }\\ & =2\text{ sec}\theta \end{array}$$

Alternate shortcut method :
$$\begin{array}{rl}& \text{Put }\theta =30^{\circ }\\ & \sqrt{\frac{1+\text{sin }30^{\circ }}{1-\text{sin }30^{\circ }}}\text{ + }\sqrt{\frac{1-\text{sin }30^{\circ }}{1+\text{sin }30^{\circ }}}\\ & \Rightarrow \sqrt{\frac{1+\frac{1}{2}}{1-\frac{1}{2}}}+\sqrt{\frac{1-\frac{1}{2}}{1+\frac{1}{2}}}\\ & \Rightarrow \sqrt{\frac{3}{1}}+\sqrt{\frac{1}{3}}\\ & \Rightarrow \frac{4}{\sqrt{3}}\end{array}$$
Now check with option by puting θ = 30°
$$\begin{array}{rl}& \text{ = 2 sec 3}{0}^{\circ }\\ & =\frac{2\times 2}{\sqrt{3}}\\ & =\frac{4}{\sqrt{3}}\end{array}$$