Correct Answer: $\frac{2}{\left(\sin ^2 \theta-\cos ^2 \theta\right)}$

Solution : $\frac{\sin \theta+\cos \theta}{\sin \theta-\cos \theta}+\frac{\sin \theta-\cos \theta}{\sin \theta+\cos \theta}$
Taking the LCM of the denominators:
= $\frac{(\sin \theta+\cos \theta)^2 + (\sin \theta-\cos \theta)^2}{\sin^2 \theta-\cos^2 \theta}$
= $\frac{(\sin^2 \theta+\cos^2 \theta+2\sin \theta \cos \theta) + (\sin^2 \theta+\cos^2 \theta-2\sin \theta \cos \theta)}{\sin^2 \theta-\cos^2 \theta}$
= $\frac{(1+2\sin \theta \cos \theta) + (1-2\sin \theta \cos \theta)}{\sin^2 \theta-\cos^2 \theta}$
= $\frac{2}{\sin^2 \theta-\cos^2 \theta}$
Hence, the correct answer is $\frac{2}{\sin^2 \theta-\cos^2 \theta}$.