cos ^2left(frac{7 pi}{8}right)+cos ^2left(fra | vedclass

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(C) We know that $\cos(\pi - 	heta) = -\cos 	heta$,so $\cos^2(\pi - 	heta) = \cos^2 	heta$. Also,$\cos(\frac{\pi}{2} - 	heta) = \sin 	heta$,so $

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$2$

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(C) We know that $\cos(\pi - 	heta) = -\cos 	heta$,so $\cos^2(\pi - 	heta) = \cos^2 	heta$. Also,$\cos(\frac{\pi}{2} - 	heta) = \sin 	heta$,so $\cos^2(\frac{\pi}{2} - 	heta) = \sin^2 	heta$. Given expression: $E = \cos^2(\frac{7\pi}{8}) + \cos^2(\frac{5\pi}{8}) + \cos^2(\frac{3\pi}{8}) + \cos^2(\frac{\pi}{8})$. Note that $\frac{7\pi}{8} = \pi - \frac{\pi}{8}$,so $\cos^2(\frac{7\pi}{8}) = \cos^2(\frac{\pi}{8})$. Note that $\frac{5\pi}{8} = \pi - \frac{3\pi}{8}$,so $\cos^2(\frac{5\pi}{8}) = \cos^2(\frac{3\pi}{8})$. Thus,$E = 2\cos^2(\frac{\pi}{8}) + 2\cos^2(\frac{3\pi}{8})$. Since $\frac{3\pi}{8} = \frac{\pi}{2} - \frac{\pi}{8}$,we have $\cos^2(\frac{3\pi}{8}) = \sin^2(\frac{\pi}{8})$. Substituting this into $E$: $E = 2\cos^2(\frac{\pi}{8}) + 2\sin^2(\frac{\pi}{8})$. $E = 2(\cos^2(\frac{\pi}{8}) + \sin^2(\frac{\pi}{8}))$. Using the identity $\sin^2 	heta + \cos^2 	heta = 1$,we get $E = 2(1) = 2$.

$\cos ^2\left(\frac{7 \pi}{8}\right)+\cos ^2\left(\frac{5 \pi}{8}\right)+\cos ^2\left(\frac{3 \pi}{8}\right)+\cos ^2\left(\frac{\pi}{8}\right)=$

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