A Bregman divergence is defined as $D(p,q) = F(p) - F(q) - < \nabla F(q), p-q>$ with F a strictly convex function of the Legendre type.
Squared Euclidian distance is a Bregman divergence, with $F(x)= ||x||^2$.
For a Cosine Distance we can show it is proportional to the squared Euclidian distance: $||p - q||^2 = ||p||^2 + ||q||^2 - 2 cos(p,q)$ which becomes $2 - 2 p^T q$ when normalizing $||p||=||q||=1$.
Does this imply the normalized Cosine similarity is also a Bregman divergence?