This is an exam problem from my analysis 1 course, and I can’t find a way to solve it.

$$lim_{xto 0} frac {arcsin(x) sqrt{sin(x)}}{tgx}$$

So far I tryed applying L’Hopital’s rule, since as x approaches zero, we get $frac{0}{0}$ as a result, and eventually I got

$$ lim_{xto 0} frac{frac{sqrt{sin(x)}}{sqrt{1-x^2}}+frac{arcsin(x)cos(x)}{2sqrt{}sin(x)}}{frac{1-x}{sqrt2x-x^2}}$$

Fast forward few steps, after trying to get rid of the double fractions, I got

$$ lim_{xto 0}frac{sqrt{2x-x^2}(2sin(x)+sqrt{1-x^2}arcsin(x)cos(x))}{2(1-x)(sqrt{1-x^2})(sqrt{sinx})} $$

And I get again $frac{0}{0}$ when I let x approach zero. I honestly doubt I should apply L’Hopital again here, and since I can’t see any other way around I am asking for help or a clue how to solve this problem.

Thanks in advance