Use the Mean Value Theorem to prove the inequality(adsbygoogle = window.adsbygoogle || []).push({});

[tex]|\sin a - \sin b| \leq |a - b|[/tex] for all a and b.

I know by the Mean Value Theorem, I can say:

[tex]\sin a - \sin b = \cos c(a - b)[/tex]

I've been trying to figure it out for awhile, but could not, so I peeked at my solution's manual. They assumed b < a, and said

[tex]|\sin a - \sin b| \leq |\cos c||b - a| \leq |a - b|[/tex]

how did they arrive at this?

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# Mean value theorem

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