Let S = {x ∈ ℝ: 0 < x < 1 and 2 tan⁻¹((1-x)/(1+x)) = cos⁻¹((1-x²)… | JEE Main 2023 Mathematics PYQ

MCQMediumJEE Main 2023 · 1 February, Shift 2Inverse Trigonometric Functions

Let $S = \{x \in \mathbb{R} : 0 < x < 1 \text{ and } 2 \tan^{-1}\left(\frac{1-x}{1+x}\right) = \cos^{-1}\left(\frac{1-x^2}{1+x^2}\right)\}$ . 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
$n(S) = 0$ .

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