Explanation

(c)
$\cos^{4}\frac{\pi}{8} + \cos^{4}{\frac{7\pi}{8} + \cos^{4}{\frac{3\pi}{8} + \cos^{4}\frac{5\pi}{8}}}$
$= \cos^{4}{\frac{\pi}{8} + \cos^{4}{\frac{\pi}{8} + \cos^{4}\left( \frac{\pi}{2} - \frac{\pi}{8} \right) + \cos^{4}\left( \frac{\pi}{2} + \frac{\pi}{8} \right)}}$
$= 2\left\lbrack \cos^{4}{\frac{\pi}{8} +}\sin^{4}\frac{\pi}{8} \right\rbrack$
$= 2\left\lbrack \left( \cos^{2}\frac{\pi}{8} + \sin^{2}\frac{\pi}{8} \right)^{2} - 2\sin^{2}{\frac{\pi}{8}\cos^{2}\frac{\pi}{8}} \right\rbrack$
$= 2\left\lbrack 1 - \frac{1}{2}\left( \sin\frac{\pi}{4} \right)^{2} \right\rbrack$
$= 2\left\lbrack 1 - \frac{1}{4} \right\rbrack = \frac{3}{2}$