Let $$S = \left\{ {x \in R:0 < x < 1\,\mathrm{and}\,2{{\tan }^{ - 1}}\left( {{{1 - x} \over {1 + x}}} \right) = {{\cos }^{ - 1}}\left( {{{1 - {x^2}} \over {1 + {x^2}}}} \right)} \right\}$$.

If $\mathrm{n(S)}$ denotes the number of elements in $\mathrm{S}$ then :

1. A $\mathrm{n}(\mathrm{S})=0$
2. B $\mathrm{n}(\mathrm{S})=1$ and only one element in $\mathrm{S}$ is less than $\frac{1}{2}$.
3. C $\mathrm{n}(\mathrm{S})=1$ and the elements in $\mathrm{S}$ is more than $\frac{1}{2}$.
4. D $\mathrm{n}(\mathrm{S})=1$ and the element in $\mathrm{S}$ is less than $\frac{1}{2}$. Correct answer