Explanation

(b)
$\sin{x > 0\ \Rightarrow x \in (0,\ \pi)}$ …(i)
$\cos{x > 0\ \Rightarrow x \in \left( \ 0,\frac{\pi}{2} \right) \cup \left( \frac{3\pi}{2},\ 2\pi \right)}$ …(ii)
From relations (i) and (ii) , we get
$x \in \left( \ 0,\frac{\pi}{2} \right)$ …(iii)
Now, $\log_{1/2}{\sin{x > \log_{1/2}{\cos x}}}$
$\Rightarrow \ \sin{x < \cos x}$ in $x \in \left( \ 0,\frac{\pi}{4} \right)$ …(iv)
From relations Eqs. (iii) and (iv), we get
$x \in \left( \ 0,\frac{\pi}{4} \right)$