Point P is any point on the inscribed circle. You must prove that
(tan(a))^2 + (tan(B))^2 = 8
I first moved point P down to the point where the square would be tangent to the curve to make the problem easier. I realized that (tan(a))^2 = (tan(b))^2 = 4 in this simplified case.
Next I separated (tan(a))^2 into
sin(a) /cos(a) *sin(a)/cos(a) =4
and from there
Then I used the law of sine to find that
[sin(a)/(2^(1/2)*AB)] = [sin(A)/(1/2AB)]
And that sin(a) = 2*2^(1/2)*sin(A)
After that I was kind of lost on what to do.
Any help would be appreciated! Thank you in advance!