(a tan u +b)^2 + (b tan u -a)^2=(a^2+b^2)sec^2u
a^2tan^2(u) + abtanu + b^2 + b^2tan^2(u) - abtanu + a^2 = (a^2+b^2)sec^2u
(a^2 + b^2)tan^2(u) + (a^2 + b^2) = (a^2+b^2)sec^2u
(a^2 + b^2)(tan^2(u) + 1) = (a^2+b^2)sec^2u
(a^2+b^2)sec^2u = (a^2+b^2)sec^2u