Let $$S = \left\{x \in R : 0 \lt x \lt 1 \text{ and } 2\tan^{-1}\left(\frac{1-x}{1+x}\right) = \cos^{-1}\left(\frac{1-x^2}{1+x^2}\right)\right\}$$. If $$n(S)$$ denotes the number of elements in $$S$$ then :

A

$$n(S) = 2$$ and only one element in $$S$$ is less than $$\frac{1}{2}$$

B

$$n(S) = 1$$ and the element in $$S$$ is more than $$\frac{1}{2}$$

C

$$n(S) = 1$$ and the element in $$S$$ is less than $$\frac{1}{2}$$

D

$$n(S) = 0$$