## Dhaka Higher Secondary 2010/3 (Secondary 2010/5)

Problem for Higher Secondary Group from Divisional Mathematical Olympiad will be solved here.
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BdMO
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Joined: Tue Jan 18, 2011 1:31 pm

### Dhaka Higher Secondary 2010/3 (Secondary 2010/5)

If $x$ is very very very small $\sin x \approx x$. An operator $S_n$ is defined such that $S_n(x)= \sin \sin \sin \cdots \sin x$ (a total of $n$ $\sin$ operators are included here). For sufficiently large $n$, $S_n(x) \approx S_{n-1}(x)$.

In that case, express $\cos (S_n(x))$ as the nearest rational value.

Moon