Let (a, b) (0,2 π) be the largest interval for which sin ⁻¹(sin θ)- cos ⁻¹(sin θ)>0, θ (0,2 π), holds. If α x²+β x+ sin ⁻¹(x²-6 x+10)+ cos ⁻¹(x²-6 x+10)=0 and α-β=b-a, then α is equal to:

Trigonometry: JEE Main 2023 Mathematics question

JEE Main 2023 · 31 Jan, Evening shift · Q4115

JEE Main 202331 Jan, Evening shiftMathematicsMediumTrigonometry118× since 2002

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}-6 x+10\right)+\cos ^{-1}\left(x^{2}-6 x+10\right)=0

and

\alpha-\beta=b-a

, then

\alpha

is equal to :

JEE Main 2023 Trigonometry Question with Solution (31 Jan Evening shift, Q4115) | JEE Arc