TITLE: Reference request for simple $q-$ identities
QUESTION [5 upvotes]: I stumbled upon the following  simple $q-$identities:
$$\frac{1}{(-q;q)_\infty}\sum \limits_{j =0}^{\infty}\frac{q^{(2r+1)j}}{(q^2;q^2)_j}=(q;q^2)_r$$
and
$$\frac{1}{(q;q^2)_\infty}\sum \limits_{j =0}^{\infty}(-1)^{j}\frac{q^{(r+1)j}}{(q;q)_j}=(-q;q)_r,$$
where $r\in\mathbb{N} $ and $\binom{r}{j}_q$ denotes a $q-$binomial coefficient. 
Probably these are well known. But where can I find such identities?  Are there tables of $q-$identities in the literature?

REPLY [5 votes]: You can use eqn. (1), (2) and (5) in this file to show the identities.