In which of the following sets the inequalities ${\sin }^{6}x+{\cos }^{6}x>\frac{5}{8}$, holds good 

${\sin }^{6}x+{\cos }^{6}x>\frac{5}{8}\Rightarrow 1-3{\sin }^{2}x{\cos }^{2}x>\frac{5}{8}$

$\Rightarrow \frac{3}{8}>3{\sin }^{2}x{\cos }^{2}x\Rightarrow {\left(2\sin x\cos x\right)}^2<\frac{5}{8}$

$\Rightarrow 2{\sin }^{2}2x-1<0\Rightarrow \cos 4x>0$

$\Rightarrow 4x\in \left(2n\pi -\frac{\pi }{2},2n\pi +\frac{\pi }{2}\right),n\in Z$

a)  $x\in \left(-\frac{\pi }{8},\frac{\pi }{8}\right)\Rightarrow 4x\in \left(-\frac{\pi }{2},\frac{\pi }{2}\right)$ holds good

b)  $x\in \left(\frac{3\pi }{8},\frac{5\pi }{8}\right)\Rightarrow 4x\in \left(\frac{3\pi }{2},\frac{5\pi }{2}\right)=\left(-\frac{\pi }{2},\frac{\pi }{2}\right)$holds good

c) $x\in \left(\frac{7\pi }{8},\frac{9\pi }{8}\right)\Rightarrow 4x\in \left(\frac{7\pi }{2},\frac{9\pi }{2}\right)=\left(-\frac{\pi }{2},\frac{\pi }{2}\right)$holds good

d) $x\in \left(\frac{\pi }{4},\frac{3\pi }{4}\right)\Rightarrow 4x\in \left(\pi ,3\pi \right)$ cross the limits