QPaperGen

We have:
\begin{align*}
\sin 75^\circ &= \sin(45^\circ + 30^\circ) \\
&= \sin 45^\circ \cos 30^\circ + \cos 45^\circ \sin 30^\circ \\
&= \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{3}}{2} + \frac{1}{\sqrt{2}} \cdot \frac{1}{2} \\
&= \frac{1}{\sqrt{2}} \cdot \left( \frac{\sqrt{3} + 1}{2} \right) \\
&= \frac{\sqrt{3} + 1}{2\sqrt{2}}
\end{align*}