Q. Let $S=\left\{x \in R: 0<x<1 \text{ and } 2\tan^{-1}\left(\frac{1-x}{1+x}\right)=\cos^{-1}\left(\frac{1-x^2}{1+x^2}\right)\right\}$. If $n(S)$ denotes the number of elements in $S$ then :
A) $\mathrm{n(S)}=2$ and only one element in $S$ is less then $\frac{1}{2}$
B) $\mathrm{n(S)}=1$ and the element in $S$ is more than $\frac{1}{2}$
C) $\mathrm{n(S)}=1$ and the element in $S$ is less then $\frac{1}{2}$
D) $\mathrm{n(S)}=0$
Explanation
The correct answer is Option C: $\mathrm{n(S)}=1$ and the element in $S$ is less then $\frac{1}{2}$.
A detailed explanation for this question is being prepared.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.