Let {\S} be the set of all solutions of the equation \cos ^{-1}(2 x)-2 \cos ^{-1} (\sqrt{1-x^2}) =\pi, x \in [-\frac{1}{2}, \frac{1}{2}]. Then \sum_{x \in {\S}} 2 \sin ^{-1} ( {\x}^2-1) is equal to [1-Feb-2023 Shift 1]

\pi- \sin ^{-1} ( {\sqrt{3}}/{4})

\pi-2 \sin ^{-1} ( {\sqrt{3}}/{4})

Inverse Trigonometric Functions

Section: Mathematics

Question : 31 of 95

Marks: +1, -0

Let S be the set of all solutions of the equation cos−1(2x)−2cos−1(√1−x2)=π,‌‌x∈[−‌

,‌

].
Then

∑

x∈S

2sin‌−1(x2−1) is equal to

[1-Feb-2023 Shift 1]

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