## 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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Please don't post problems (by starting a topic) in the "Higher Secondary: Solved" forum. This forum is only for showcasing the problems for the convenience of the users. You can post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
BdMO
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### 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
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### Re: Dhaka Higher Secondary 2010/3 (Secondary 2010/5)

"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.