Simplifier les expressions suivantes
1
\(\sin(2\Arcsin x)\),
2
\(\cos(2\Arccos x)\),
3
\(\sin^2\left(\frac{\Arccos x}{2}\right)\),
4
\(\ln(\sqrt{x^2+1}+x)+\ln(\sqrt{x^2+1}-x)\),
5
\(\Argsh\left(\frac{x^2-1}{2x}\right)\),
6
\(\Argch(2x^2-1)\),
7
\(\Argth\left(\sqrt{\frac{\ch x-1}{\ch x+1}}\right)\),
8
\(\frac{\ch(\ln x)+\sh(\ln x)}{x}\).