If α ≤ 2sin⁻¹ x + cos⁻¹ x ≤ β, then (α, β) is:

Answer: (a) $(0, \pi)$ $2\sin^{-1}x+\cos^{-1}x=\sin^{-1}x+\left(\sin^{-1}x+\cos^{-1}x\right)=\sin^{-1}x+\frac{\pi}{2}$. For $x\in[-1,1]$, $\sin^{-1}x\in[-\frac{\pi}{2},\frac{\pi}{2}]$, so the expression lies in $[0,\pi]$. Hence $(\alpha,\beta)=(0,\pi)$.