A quick graph shows the solution to be pi/4.
This is pretty obvious because sin(pi/4)=cos(pi/4) and tan(pi/4)=cot(pi/4).
A unit circle approach doesn't seem to help
y^(y/x) = x^(x/y) where x^2+y^2=1
If you sub y=sqrt(1x^2) then WolframAlpha won't even give the exact solutionx=sqrt(1/2).

Posted by Jer
on 20240825 12:00:59 