I was wondering if someone can verify (or not) the correctness of the following function?

$$\frac{1}{\sinh^2X}=\coth^2X-1$$

I saw it in a paper but I am weak in math, so I am unsure if it is correct or not. I assume that the author took the following two functions in consideration:

$$\operatorname{csch}^2X=\coth^2X-1$$
$$\operatorname{csch}X=\frac{1}{\sinh X}$$

Thank you in advance.