I assume you mean (1 + tan^2u)(1 - sin^2u) = 1 so I solved it like that
because tanu = sinu / cosu ⇒ tan^2u = sin^2u / con^2u
(1 + sin^2u/cos^2u)(1 - sin^2u) =
(cos^2u/cos^2u + sin^2u/cos^2u)(1 - sin^2u) =
((cos^2u + sin^2u)/(cos^2u)) (1 - sin^2u) =
and because cos^2u + sin^2u = 1 we'll have
(1/(cos^2u)) (1 - sin^2u) =
1/(cos^2u) - sin^2u/(cos^2u) =
(1 - sin^2u) / (cos^2u) =
notice that 1 - sin^2u is equal to cos^2u
cos^2u / cos^2u = 1
