exo7 5095

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

\(\frac{\ch(\ln x)+\sh(\ln x)}{x}\).