Let S be the set of all solutions of the equation \({\cos }^{-1}(2x)-2{\cos }^{-1}\left(\sqrt{1-{x}^{2}}\right)=\pi ,x\in \left[-\frac{1}{2},\frac{1}{2}\right]\text{. }\) Then \(\sum _{x\in S}2{\sin }^{-1}\left({x}^{2}-1\right)\) is equal to

[JEE Main 2023, 1 Feb (Shift 1)]

Question

Let S be the set of all solutions of the equation \({\cos }^{-1}(2x)-2{\cos }^{-1}\left(\sqrt{1-{x}^{2}}\right)=\pi ,x\in \left[-\frac{1}{2},\frac{1}{2}\right]\text{. }\) Then \(\sum _{x\in S}2{\sin }^{-1}\left({x}^{2}-1\right)\) is equal to

[JEE Main 2023, 1 Feb (Shift 1)]

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Let S be the set of all solutions of the equation \({\cos }^{-1}(2x)-2{\cos }^{-1}\left(\sqrt{1-{x}^{2}}\right)=\pi ,x\i…

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