Answer
$\cos y$
Work Step by Step
Given expression is-
$ \frac{1 + \cos y}{1 + \sec y} $
= $ \frac{1 + \cos y}{1 + \frac{1}{\cos y}} $
= $ \frac{1 + \cos y}{\frac{\cos y + 1}{\cos y}} $
= $ (1 + \cos y) . \frac{\cos y}{(\cos y + 1)} $
= $\cos y$
