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Possible Duplicate:
Crafty solutions to the following limit

A problem in a trivium was:

$$\lim\limits_{x \to 0} \frac{\sin(\tan x)-\tan(\sin x)}{\arcsin(\arctan x)-\arctan(\arcsin x)}$$

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    If I am not mistaken this is a problem from Arnold. A google search or something can give a quick answer on this. The result is -1.2012-02-19
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    @ChangweiZhou : Who is Arnold?2012-02-19
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    @V.I.Arnold. Also apologize for confusing the sign.2012-02-19
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    I knew I'd seen this before *here*: [duplicate](http://math.stackexchange.com/q/80364/742).2012-02-19

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Check this article:

https://mathoverflow.net/questions/20696/a-question-regarding-a-claim-of-v-i-arnold

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    Especially Robert Israel’s answer, which makes the right intuition crystal clear.2012-02-19
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    That's called a classic trick question-it tricks you into overthinking the problem. This is why recognizing patterns is so important in practical problem solving!2012-02-19