Inverse Trigonometric Functions

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 :