precalculus simplify identities

Question

Simplify to a single trig function.

Answer 1

(1 + sec)(1+cos) =

1 + cos + sec + 1 <--- FOIL

2 + cos + sec

(2cos + cos^2 + 1)/cos <--- common denominator is cosine

(cos^2 + 2cos + 1)/cos

(cos +1)^2/cos <--- factors