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

Mathematics Question from JEE Main 2023 · 1 February, Shift 1

Let SS be the set of all solutions of the equation cos⁡−1(2x)−2cos⁡−1(1−x2)=π,x∈[−12,12].\cos^{-1}(2x) - 2\cos^{-1}(\sqrt{1 - x^2}) = \pi, \quad x \in \left[ -\frac{1}{2}, \frac{1}{2} \right] . Then ∑x∈S2sin⁡−1(x2−1)\sum_{x \in S} 2 \sin^{-1}(x^2 - 1) is equal to:

  • A

    00

  • B

    −2π3\frac{-2\pi}{3}

  • C

    π−sin⁡−1(34)\pi - \sin^{-1} \left( \frac{\sqrt{3}}{4} \right)

  • D

    π−2sin⁡−1(34)\pi - 2\sin^{-1} \left( \frac{\sqrt{3}}{4} \right)

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