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

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 ?

• You're correct. Multiplication is commutative. The question was badly designed. – Michael Lugo Jan 3 at 15:10
• Either that or it was a misprint or sejy misread it. From the information in the question, we cannot determine which of these three possibilities holds. – GEdgar Jan 3 at 15:34

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 $$x,y\in \mathbb{C}$$.