$ 2 \sinh(z)=\exp(z)-\exp(-z)$;

$ 2 \cosh(z)=\exp(z)+\exp(-z)$

where $z \in \mathbb{C} $

$$\sin(z) := \sum_{k=0}^{\infty}\frac{(-1)^k}{2k+1!} z^{2k+1}$$

$$\cos(z) := \sum_{k=0}^{\infty}\frac{(-1)^k}{2k!} z^{2k}$$

I guess that I have to use a trigonometrical identity, but I don't know which one and is that step equivalent to use it for hyperbolic functions? Thank in advance for your help.