Simplify and write the trigonometric expression in terms of sine and cosine:
\[
\frac{1+\cos y}{1+\sec y}=
\]
Simplify the expression: \(\boxed{\cos y}\)
Step 1 :Rewrite the secant function in terms of cosine: \(\frac{1 + \cos y}{1 + \frac{1}{\cos y}}\)
Step 2 :Simplify the expression: \(\boxed{\cos y}\)