Verify the identity. Show your work.

(1 + tan2u) (1 - sin2u) = 1

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