Question 238105
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I'm not sure what you mean by "solve this."  There is no equals sign and no variable.


The only thing I can think to do with this is to calculate a numerical approximation.  First recognize that:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cos(2x)\ =\ \cos^2(x)\ -\ \sin^2(x)]


Therefore


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sin^2(x)\ -\ \cos^2(x)\ =\ -\cos(2x)]


hence


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sin^2\left(\frac{2\pi}{5}\right)\ -\ \cos^2\left(\frac{2\pi}{5}\right)\ =\ -\cos\left(\frac{4\pi}{5}\right)\ \approx\ 0.809]


But not sure where you want to go from here.



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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