JEE Main 20231 Feb, Evening shiftMathematicsMediumTrigonometry118× since 2002Let S={x∈R:0<x<1 and 2tan−1(1−x1+x)=cos−1(1−x21+x2)}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\}S={x∈R:0<x<1and2tan−1(1+x1−x)=cos−1(1+x21−x2)}. If n(S)\mathrm{n(S)}n(S) denotes the number of elements in S\mathrm{S}S then :AOption A. n(S)=0\mathrm{n}(\mathrm{S})=0n(S)=0BOption B. n(S)=1\mathrm{n}(\mathrm{S})=1n(S)=1 and only one element in S\mathrm{S}S is less than 12\frac{1}{2}21.COption C. n(S)=1\mathrm{n}(\mathrm{S})=1n(S)=1 and the elements in S\mathrm{S}S is more than 12\frac{1}{2}21.DOption D. n(S)=1\mathrm{n}(\mathrm{S})=1n(S)=1 and the element in S\mathrm{S}S is less than 12\frac{1}{2}21.CheckSkip · show solution
