Verify the identity. Show your work.

Question

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

Answer 1

I assumed that
(1 + tan^2 u)(1 - sin^2 u) = 1

Note that (1 + tan^2 u) = sec^2 u. [pythagorean identity]
And that (1 - sin^2 u) = cos^2 u. [pythagorean identity, from cos^2 u + sin^2 u = 1]
Thus,
( sec^2 u )( cos^2 u )= 1

Note that sec u = 1 / cos u,
(1 / cos u)^2 (cos^2 u) = 1
cos^2 u / cos^2 u = 1
1 = 1

Answer 2

Yeah I had this answer , just making sure , Thank you :)