Use Mean value Theorem To prove in equality | sin a - sin b | ≤ |a-b| for all a and b

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Use the Mean Value Theorem to prove that |sin(a)-sin(b)| ≤ |a-b| for all real values of a and b, a≠b Use the Mean Value Theorem to prove that |sin(a)-sin(b)| ≤ |a-b| for all real values of a and b, a≠b
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I don I don't get the intuition of using mean value theorem to prove inequalities. Reddit r/calculus
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