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Inverse Trigonometric Functions question

2023 · 1 Feb · Shift 1 · Q23

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PYQ Library
JEE Main
Mathematics
Inverse Trigonometric Functions
2023 · 1 Feb · Shift 1 · Q23

Inverse Trigonometric Functions question

2023 · 1 Feb · Shift 1 · Q23

JEE MainMathematicsInverse Trigonometric FunctionsMCQ+4 / −1

Let

S

be the set of all solutions of the equation

\cos ^{-1}(2 x)-2 \cos ^{-1}\left(\sqrt{1-x^{2}}\right)=\pi, x \in\left[-\frac{1}{2}, \frac{1}{2}\right]

. Then

\sum_{x \in S} 2 \sin ^{-1}\left(x^{2}-1\right)

is equal to :

A
$\pi-2 \sin ^{-1}\left(\frac{\sqrt{3}}{4}\right)$
B
$\pi-\sin ^{-1}\left(\frac{\sqrt{3}}{4}\right)$
C
$\frac{-2 \pi}{3}$
D
None

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