∫ (cos 2 x)/(cos x) d x is equal to

$I=\int \frac{2 \cos ^2 x-1}{\cos x} d x$

$I=\int(2 \cos x-\sec x) d x=2 \int \cos x d x-\int \sec x d x$

= 2 sin x – log| sec x + tan x| + c

Hence (4) is the correct answer.