Answer
2 $ \sec u $
Work Step by Step
Given expression is-
$ \frac{1 + \sin u}{\cos u} + \frac{\cos u}{1 + \sin u} $
= $\frac{(1 + \sin u)^{2} + \cos^{2} u}{\cos u(1 + \sin u)} $
= $\frac{1 + 2\sin u+ \sin^{2} u + \cos^{2} u}{\cos u(1 + \sin u)} $
= $\frac{1 + 2\sin u+ 1}{\cos u(1 + \sin u)} $
(using first Pythagorean identity)
= $\frac{2 + 2\sin u}{\cos u(1 + \sin u)} $
= $\frac{2(1 + \sin u)}{\cos u(1 + \sin u)} $
= $2 . \frac{1}{\cos u} $
= $2 \sec u $
