The set of values of x for which $tan^{-1}\frac{x}{\sqrt{1-x^2}}= sin^{-1} x $ holds , is

R (-1,1) [0, 1] [-1, 0]

(-1,1)

We observe that RHS is defined for all x ∈ [-1,1] whereas LHS is meaningful for -1 < x < 1. Also, for x ∈(-1, 1), we have $tan^{-1}\left(\frac{x}{\sqrt{1-x^2}}\right)$ $=tan^{-1}\left(\frac{sin \theta }{\cos\theta }\right)$, where x = sin θ $= θ = sin^{-1} x $