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.
Dhaka Higher Secondary 2010/3 (Secondary 2010/5)
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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.
Re: Dhaka Higher Secondary 2010/3 (Secondary 2010/5)
Solved here: viewtopic.php?p=1314#p1314
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learn how to write equations, and don't forget to read Forum Guide and Rules.