alleryThe range of $\cos^{-1}(x)$ is
A$[0, \pi]$
B$\mathbb{R}$
C$[-\tfrac{\pi}{2}, \tfrac{\pi}{2}]$
D$(-\pi, \pi)$
Answer & Solution
Correct answer: A. $[0, \pi]$
By the standard principal-value convention, $\cos^{-1}$ returns angles in $[0, \pi]$ — the interval where cosine is monotonically decreasing and hits every value in $[-1,1]$ exactly once.
**Option A is the range of $\sin^{-1}$ and $\tan^{-1}$, not $\cos^{-1}$.**
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