q-trigonometric formulas

Question

Let the q-exponential function be:

$$exp_q(x)=1+\sum_{n\geq 1}\frac{x^n}{(1-q)\ldots(1-q^n)}$$

If $ q.xx'=x'x$, then we have the q-trigonometric formulas:

$$cos_q (x+x')=cos_q (x)cos_q (x')-sin_q (x)sin_q (x')$$

$$sin_q (x+x')= sin_q (x) cos_q (x')+ cos_q (x) sin_q (x')$$

Can we make q-trigonometry with these formulas?