Prove inequality using Mean Value Theorem 2

Asked May 16 '18 at 07:32

Active May 16 '18 at 08:54

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$|\cos ^2(b) - \cos^2(a)| > \frac{1}{4}|b-a|$ for all $a,b$ within $(\frac{\pi}{4}, \frac{\pi}{3})$ where $a$ is not equal to $b$. I have done a few other examples and proved them correctly using MVT but this is causing me difficulty.

edited May 16 '18 at 08:54

asked May 16 '18 at 07:32

Adam Jones

Why complex-analysis? Why proof-verification? – José Carlos Santos May 16 '18 at 07:44
Mean Value Theorem is in Complex analysis course, Proof-verification was a misclick. Also was no tag for Mean value theorem to be seen. – Adam Jones May 16 '18 at 07:48
$\cos^2b-\cos^2a=\frac12(\cos2b-\cos2a)=-\sin(2c)(b-a)$ and then find a lower bound on $\sin 2c$ in the given interval. This may seem complicated, but is all real analysis, not complex numbers here. – Lutz Lehmann May 16 '18 at 08:48
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Why $1/4?$ Im getting $\sqrt 3/2.$ And what is MVT 2? – zhw. May 16 '18 at 14:11

Prove inequality using Mean Value Theorem 2

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