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If \(\theta \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\), then \(\cos ^{-1}(\sin \theta)\) is equal to
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Verified Answer
The correct answer is:
\(\frac{\pi}{2}-\theta\)
\(\begin{aligned}
& \theta \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right], \cos ^{-1}(\sin \theta)=? \\
& \Rightarrow \quad \cos ^{-1}\left[\cos \left(\frac{\pi}{2}-\theta\right)\right]=\left(\frac{\pi}{2}-\theta\right)
\end{aligned}\)
& \theta \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right], \cos ^{-1}(\sin \theta)=? \\
& \Rightarrow \quad \cos ^{-1}\left[\cos \left(\frac{\pi}{2}-\theta\right)\right]=\left(\frac{\pi}{2}-\theta\right)
\end{aligned}\)
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