When are $x'$ and $y'$ set equal to $0$ during this proof? My teacher said they were, but it seems to me like their coefficient is set equal to $0$ so they disappear. Please help.
This is the proof:
https://ipfs.io/ipfs/QmXoypizjW3WknFiJnKLwHCnL72vedxjQkDDP1mXWo6uco/wiki/Rotation_of_axes.html
$x'$ and $y'$ are not being set to zero in the proof. The theta is being chosen cleverly such that $B'$ is 0 thus the term $B'x'y'$ becomes zero and disappears. The $B'$ becomes zero because $\cos(2\theta) = \cos^2 \theta -\sin^2 \theta$ and $\sin (2 \theta) = 2 \sin \theta \cos \theta$ thus $$ \cot(2 \theta) = \frac{\cos(2\theta)}{\sin (2 \theta)} =\frac{\cos^2 \theta -\sin^2 \theta}{2 \sin \theta \cos \theta} $$ If you set this equal to $\frac{A-C}{B}$ then its pretty easy to see that $B'$ becomes zero.