I've recently been going over the mean value and intermediate value theorems, however I'm not sure where to start on this.
2026-03-25 12:29:32.1774441772
Show that $|\sin{a}-\sin{b}| \le |a-b| $ for all $a$ and $b$
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The mean value theorem will do just fine. Setting $f(x) = \sin(x)$, note that $$ |f(x) - f(y)| = |f'(c)||x - y| $$ for some value $c$. Can we find an upper bound for $|f'(c)|$?