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Inverse Trigonometric Functions question

2023 · 1 Feb · Shift 2 · Q37

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PYQ Library
JEE Main
Mathematics
Inverse Trigonometric Functions
2023 · 1 Feb · Shift 2 · Q37

Inverse Trigonometric Functions question

2023 · 1 Feb · Shift 2 · Q37

JEE MainMathematicsInverse Trigonometric FunctionsMCQ+4 / −1

Let

S = \left\{ x \in R: 0 \lt x \lt 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

\mathrm{n(S)}

denotes the number of elements in

\mathrm{S}

then :

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

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