[Trigonometric Identities.]

Find the relationship between $\arcsin \cos \arcsin x$ and $\arccos \sin \arccos x$.

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Answer: $\arcsin \cos \arcsin x+\arccos \sin \arccos x=\frac{\pi}{2}$. Let $\arcsin \cos \arcsin x=\alpha$ and $\arccos \sin \arccos x=\beta$. Then $0 \leq \alpha$