What is Cosecant inverse of $x$ equal to?

Question

What is $\csc^{-1}x$ = equal to?

Could anyone tell me the answer to this question?

This question was given to me exactly the same way I have written it here, they didn't ask for anything else but the value.

Answer 1

$$\csc^{-1}(x)=\sin^{-1}\left(\frac{1}{x}\right)$$

Answer 2

To the power of negative one has two possible meanings (without context):

• reciprocal - i.e. $\csc^{-1}x = \sin x$
• inverse - i.e. $\csc^{-1}x = \operatorname{arccsc} x$

Assuming you have only recently starting doing $cosec$ I would say the first option is more likely what you were expected to give.