Answer
$\dfrac{\sqrt{6}+\sqrt{2}}{4}$
Work Step by Step
Addition formula
$$\sin{(A+B)}= \sin{A} \cos{B} +\cos{A} \sin{B}$$
$\therefore \sin{\left(\dfrac{\pi}{4}+\dfrac{\pi}{3}\right)} = \sin{\left(\dfrac{\pi}{4} \right)} \cos{\left(\dfrac{\pi}{3} \right)} + \cos{\left(\dfrac{\pi}{4} \right)} \sin{\left(\dfrac{\pi}{3} \right)}$
$\sin{\left(\dfrac{\pi}{4}+\dfrac{\pi}{3}\right)} =\dfrac{\sqrt{2}}{2} \times \dfrac{1}{2}+ \dfrac{\sqrt{2}}{2} \times \dfrac{\sqrt{3}}{2}$
$\sin{\left(\dfrac{\pi}{4}+\dfrac{\pi}{3}\right)} = \dfrac{\sqrt{6}+\sqrt{2}}{4}$
