Range and Domain of Functions

never mind about the second one ... its probably editor's carelessness

But i really need help with the first one

I've got this so far:

$|sin^{-1}sin x| \geq cos^{-1}cos x$

$|sin^{-1}sin x| \ = \ sin^{-1}sin x, \ when \ sin^{-1}sin x \geq 0 \implies sin x\geq0 \implies x \in [0,\pi] \ in \ [0,2\pi]$

$= \ -sin^{-1}sin x \ when \ sin^{-1}sin x \leq 0 \implies sin x \leq 0 \implies x \in [\pi,2\pi] \ in \ [0,2\pi]$

so

$sin^{-1}sin x \geq cos^{-1}cos x \ \forall \ x \in [0,\pi]$

$-sin^{-1}sin x \geq cos^{-1}cos x \ \forall \ x \in [\pi,2\pi]$

Now what ???

Please Reply ... i have nothing new to post now ... and the moderator will kill me if i again dump in a thread