I do not know if i am going to help you, but:

Why dont you try to expand the identity as follow:

From binomial expansion we have:

And then we have the equality:

From there i have nothing more...

Some ideas:

If we rise both sides to a expand the right side and the again rise to a,

mayby we could compare the addition terms.

or

if we try to simplify left side by divisions of 2.

again i do not know if this helps to prove (or disprove) your identity.