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Finding value of $\lim_{n\rightarrow \infty}\sin(\sin(\sin(.......(\sin \left(\frac{\pi}{2}\right))))$

Attempt: $\displaystyle \sin(\frac{\pi}{2})=1$

so $\displaystyle \sin(\sin \frac{\pi}{2})= \sin(1)$

could some help me how to solve it,thanks

DXT
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  • The limit is not a function of $n$. Is $n$ the number of times that sin() is applied? – Hugh Feb 23 '19 at 13:29

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