Answer
$\dfrac{\sqrt{3}+1}{2}$
Work Step by Step
$\sin \frac{2 \pi}{3}-\cos \frac{4 \pi}{3}$
$=\sin \frac{2 \times 180}{3}-\cos \frac{4 \times 180}{3}$
$=\sin 120-\cos 240^{\circ}$
$=\sin (180-60)^{\circ}-\cos (180+60)$
$=\sin 60^{\circ}-\left(-\cos 60^{\circ}\right)$
$=\dfrac{\sqrt{3}}{2}+\dfrac{1}{2}$
$=\dfrac{\sqrt{3}+1}{2}$
