To my eyes, this is not actually Brooks, but just someone who merely resembles her. (The face doesn't quite resemble the actress, and her partially exposed breast seems too big. Brooks had small breasts, like "little pears.") Many Ziegfeld Follies girls wore bobs, and many posed for this sort of cheesecake photo.
What do you think ? There are a couple of copies of this image for sale, both from the same seller. Here is a link for those interested.