Explanation

(b)
$f(x) = \sin^{4}{x + \cos^{4}x}$
$\ \ \ \ \ \ \ \ \ = {{(sin}^{2}{xcos^{2}x)}}^{2} - 2\sin^{2}{x\ cos^{2}x}$
$\ \ \ \ \ \ \ \ \ = 1 - \frac{1}{2}\left( \sin{2x} \right)^{2}$
$\ \ \ \ \ \ \ \ = \frac{3}{4} + \frac{1}{4}\cos{4x}$
$\therefore$ The period of $f(x) = \frac{2\pi}{4} = \frac{\pi}{2}$