Question

I need to know if these two statements are true or false And if they’re not what is the explanation

Answer 1

sin⁻¹ (sin x) = x TRUE

tan (tan⁻¹ x) = x TRUE

Step-by-step explanation

sin⁻¹ (sin x) = x

This statement is TRUE.

Reason: The arcsin function is the inverse of the sine function. It returns the angle whose sine is a given number. That is:

`\begin{gathered} \sin ^(-1)(\sin x)=x \\ \Rightarrow(1)/(\sin)*\sin x=x \\ (\sin )/(\sin )x=x \\ x=x \end{gathered}`

tan (tan⁻¹ x) = x

The statement is TRUE.

Reason: The tangent of the arctan of an angle returns the angle. This implies

`\begin{gathered} \tan (\tan ^(-1)x)=x \\ \Rightarrow\tan ((x)/(\tan ))=x \\ (\tan )/(\tan )x=x \\ x=x \end{gathered}`