Explanation

(d)
$2\sin{x\cos{x = \frac{1}{2}}}$
$\Rightarrow \ \sin{2x = \frac{1}{2} = \sin\frac{\pi}{6}}$
$\Rightarrow \ \ 2x = n\pi + ( - 1)^{n}\frac{\pi}{6}$
$\Rightarrow \ \ x = \frac{n\pi}{2} + ( - 1)^{n}\frac{\pi}{12}$
For $x \in \left( 0,\frac{\pi}{2} \right)$
$x = \frac{\pi}{12}$ $(n = 0)$