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MCQMediumJEE Main 2023 · 31 January, Shift 2Inverse Trigonometric Functions

Mathematics Question from JEE Main 2023 · 31 January, Shift 2

Let (a,b)⊂(0,2π)(a, b) \subset (0, 2\pi) be the largest interval for which sin⁡−1(sin⁡θ)−cos⁡−1(sin⁡θ)>0,θ∈(0,2π)\sin^{-1}(\sin \theta) - \cos^{-1}(\sin \theta) > 0, \quad \theta \in (0, 2\pi) holds. If αx2+βx+sin⁡−1(x2−6x+10)+cos⁡−1(x2−6x+10)=0\alpha x^2 + \beta x + \sin^{-1}\left( x^2 - 6x + 10 \right) + \cos^{-1}\left( x^2 - 6x + 10 \right) = 0 and α−β=b−a\alpha - \beta = b - a, then α\alpha is equal to:

  • A

    π48\frac{\pi}{48}

  • B

    π16\frac{\pi}{16}

  • C

    π12\frac{\pi}{12}

  • D

    π8\frac{\pi}{8}

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