QPaperGen

\begin{align*}
\text{LHS} &= \cos\left( \frac{\pi}{4} - x \right)\cos\left( \frac{\pi}{4} - y \right) - \sin\left( \frac{\pi}{4} - x \right)\sin\left( \frac{\pi}{4} - y \right) \\
&= \cos\left[ \left( \frac{\pi}{4} - x \right) + \left( \frac{\pi}{4} - y \right) \right] \\
&= \cos\left( \frac{\pi}{2} - (x + y) \right) \\
&= \sin(x + y) = \text{RHS} \qquad(\textbf{Hence proved).}
\end{align*}