Question

Given the standard restricted domains, which of the following relationships does not hold for x=-1? (Assume angles are in radians.)

Answer 1

`D:\text{ arccos\lparen cos\lparen-1\rparen\rparen= 1}`

Step-by-step explanation:

From the restricted domain, we want to check for the relationship that does not hold

All we have to do here is to substitute the value -1 for x, after which we evaluate each of the given equations

We proceed as follows:

`\begin{gathered} a)\text{ sin\lparen}\sin^(-1)(-1))\text{ = -1} \\ b)\text{ arcsin\lparen sin\lparen-1\rparen\rparen = -1} \\ c)\text{ cos\lparen arc cos \lparen-1\rparen\rparen = -1} \\ d)\text{ arc cos\lparen cos\lparen-1\rparen\rparen = 1} \\ e)\text{ tan\lparen arc tan\lparen-1\rparen\rparen = -1} \\ f)\text{ arctan\lparen tan\lparen-1\rparen\rparen = -1} \end{gathered}`

The correct option is thus D