mean value theorem problem

[Guest]

Can you help me for this question please?

Questions says

For all the real number x and y, use mean value theorem to show that inequation |sinx-siny|[tex]\le[/tex] |x-y| is valid.

This is now english math problem, so maybe translation is bit complicated. sorry.

[Guest]

Are you clear in what the "mean value theorem" is?

"If f(x) is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) then there exist c in (a, b) such that [tex]\frac{f(b)- f(a)}{b- a}= f'(c)[/tex]."

For this problem, take f(x)= sin(x). f'(x)= cos(x) and, for all x, [tex]-1\le cos(x)\le 1[/tex].