$\cos^{-1}(-x) = $

For $x \in [-1, 1]$: $\cos^{-1}(-x) = \pi - \cos^{-1}(x)$. Reason: $\cos(\pi - y) = -\cos y$. Setting $y = \cos^{-1}(x)$ gives $\cos(\pi - \cos^{-1} x) = -x$ so applying $\cos^{-1}$ to both sides (both LHS and target lie in $[0, \pi]$) gives the result. Compare $\sin^{-1}(-x) = -\sin^{-1}(x)$ (option A would apply here). The odd-function form works for $\sin^{-1}$ but not $\cos^{-1}$ because their principal ranges differ.