Answer
$\dfrac{\sqrt{2}}{2}$
Work Step by Step
$\sin{\alpha} - \sin{\beta} = 2 \cos{(\dfrac{\alpha+\beta}{2})} \sin{\dfrac{\alpha-\beta}{2})} $
$\sin{\dfrac{7\pi}{12}} - \sin{\dfrac{\pi}{12}} = 2 \cos{\dfrac{\pi}{3}} \sin{\dfrac{\pi}{4}} = \dfrac{\sqrt{2}}{2}$