Answer
$$\frac{\sqrt{6}+\sqrt{2}}{4}$$
Work Step by Step
Since
$$\sin(x+y)= \sin x\cos y+\cos x\sin y $$
Then
\begin{align*}
\sin(75^{\circ})&= \sin(45^{\circ}+30^{\circ})\\
&=\sin 45^{\circ}\cos 30^{\circ}+\cos45^{\circ}\sin 30^{\circ}\\
&= \frac{\sqrt{3}\sqrt{2}}{4}\sin \theta + \frac{\sqrt{2}}{4}\cos \theta\\
&= \frac{\sqrt{6}+\sqrt{2}}{4}
\end{align*}
