How to show the following summation is true?

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SUMMARY

The summation ∑(-1)^n * cos(nx) / n^2 is proven to equal (3x^2 - π^2)/12. This conclusion is derived using the known result that ∑_{n=1}^{∞} 1/n^2 = π^2/6. The proof involves techniques from Fourier series and series convergence, specifically leveraging properties of alternating series and trigonometric identities.

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I need to prove that the following summation is true:

∑(-1)^n * cos(nx) / n^2 = (3x^2 - π^2)/12

How would I tackle this problem?
 
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Hint: [itex]\sum_{n=1}^{\infty}\frac{1}{n^{2}}=\frac{\pi^{2}}{6}[/itex]
 

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