My Cousin's Challenge: Solve a Tough Limit Problem

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My cousin challenges me with a tough limit problem.

Compute the limit as x->0 of (sin(tanx)-tan(sinx))/(arcsin(arctanx)-arctan(arcsinx)).

This limit seems impossible to do.

I used L'Hopital's rule but it didn't help at all.

Can anyone find a way to do it?
 

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Expand the numerator and the denominator as Taylor series up to the first significant term.