Option A
Since $\csc^2\theta - \cot^2\theta = 1$, we get $(\csc\theta - \cot\theta)(\csc\theta + \cot\theta) = 1$, so the two expressions are indeed reciprocals of each other. Both A and R are true, and R directly explains A.
The identity $\csc^2\theta - \cot^2\theta = 1$ (from the source, §8.4) can be factorised as a difference of squares to give $(\csc\theta - \cot\theta)(\csc\theta + \cot\theta) = 1$, which is precisely what "reciprocal of each other" means. So R is the correct and complete explanation of A — choose Option A.