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Math Help - Proof using Lagrange M Mean Value Theorem

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    Proof using Lagrange M Mean Value Theorem

    Using Lagrange Mean Value Theorem prove that for every
    a,b are real numbers on has |sina-sinb|<or=|a-b|
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    Quote Originally Posted by amm345 View Post
    Using Lagrange Mean Value Theorem prove that for every
    a,b are real numbers on has |sina-sinb|<or=|a-b|
    Let a,b\in\mathbb{R}. We know by the MVT that \frac{\sin(a)-\sin(b)}{a-b}=f'(c)\implies \left|\sin(a)-\sin(b)\right|\leqslant |f'(c)||a-b| for some c\in(a,b). But, f'(c)=\cos(c)\leqslant1 so that \left|\sin(a)-\sin(b)\right|=\left|\cos(c)\right||a-b|\leqslant |a-b|
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