Simplify the expression

$\cos^2(\frac{\pi}{4}-\frac x2)-\sin^2(\frac{\pi}{4}-\frac x2)=\cos[2(\frac{\pi}{4}-\frac x2)]=\cos(\frac{\pi}{2}-x)=\boxed{\sin x}$

$\begin{aligned} y & = \cos^2 \left(\frac \pi 4 - \frac x2 \right) - \sin^2 \left(\frac \pi 4 - \frac x2 \right) & \small \color{#3D99F6} \text{Note that }\cos^2 A - \sin^2 A = \cos 2A \\ & = \cos \left(\frac \pi 2 - x \right) \\ & = \boxed{\sin x} \end{aligned}$

The graph for the given expression is:

The graph for a) is:

The graph for b) is:

The graph for c) is:

The graph for d) is:

It can be clearly seen that the graph for the given expression and the graph for the expression at d) are the same.