Let $(a,b)\subset (0,2\pi )$ be the largest interval for which${\sin }^{-1}(\sin \theta )-{\cos }^{-1}(\sin \theta )0,\theta \in (0,2\pi )$ holds. If $\alpha {x}^{2}+\beta x+{\sin }^{-1}\left({x}^{2}-6x+10\right)+{\cos }^{-1}\left({x}^{2}-6x+10\right)=0$ and $\alpha -\beta =b-a$, then $\alpha$ is equal to: [JEE Main 2023, 31 Jan (Shift 2)]

Question

Let $(a,b)\subset (0,2\pi )$ be the largest interval for which${\sin }^{-1}(\sin \theta )-{\cos }^{-1}(\sin \theta )>0,\theta \in (0,2\pi )$ holds. If $\alpha {x}^{2}+\beta x+{\sin }^{-1}\left({x}^{2}-6x+10\right)+{\cos }^{-1}\left({x}^{2}-6x+10\right)=0$ and $\alpha -\beta =b-a$, then $\alpha$ is equal to: [JEE Main 2023, 31 Jan (Shift 2)]

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Let \((a,b)\subset (0,2\pi )\) be the largest interval for which\({\sin }^{-1}(\sin \theta )-{\cos }^{-1}(\sin \theta )>…

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