(Solved) How are those trigonometric values equivalent?

[white plume]

With x and y real numbers, can you explain this? I don't really get how it uses the cos^2(x)=sin^2(x) formula, and why the hell does the x becomes a y (and reverse) for some reason.
$\cos^2(x) + \sin^2(y)=1 \iff \cos^2(x) = 1 - \sin^2(x) \iff \cos^2(x) = \cos^2(y)$

[white plume]

$\cos^2(x) + \sin^2(y)=1 \iff \cos^2(x) = 1 - \sin^2(x) \iff \cos^2(x) = \cos^2(y)$

[unreal crater]

jeuxjeux20

[white plume]

oh wait, it was a typo lol, got it

[marsh jetty]

(Solved) How are those trigonometric values equivalent?

[white plume]

.solved