Is $ \sinh(x) \sinh(y)=\sinh(y) \sinh(x)$?

Question

Is $ \sinh(x) \sinh(y)=\sinh(y) \sinh(x)$? While evaluation a question on multiple integral I have got answer $4\sinh(3) \sinh(1)$.

It was a multiple choice questions with

a) $4\sinh(3) \sinh(1)$

b) $4\sinh(1)\sinh(3)$

I think both a and b option are correct since $\sinh(1)$ ,$\sinh(3)$ is multiplication of numbers it should commute but in answer option a is mention .

Am I correct both option is correct ? If wrong please explain why ?

Answer 1

Yes: $\sinh:\mathbb{C}\to \mathbb{C}$ so that $\sinh(x),\sinh(y)\in \mathbb{C}$. Thus, by commutativity of multiplication in $\mathbb{C}$, $\sinh(x)\sinh(y)=\sinh(y)\sinh(x)$ for any $x,y\in \mathbb{C}$.