Answer
sin⁻¹ (sin x) = x TRUE
tan (tan⁻¹ x) = x TRUE
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:
[tex]\begin{gathered} \sin ^{-1}(\sin x)=x \\ \Rightarrow\frac{1}{\sin}\times\sin x=x \\ \frac{\sin }{\sin }x=x \\ x=x \end{gathered}[/tex]
tan (tan⁻¹ x) = x
The statement is TRUE.
Reason: The tangent of the arctan of an angle returns the angle. This implies
[tex]\begin{gathered} \tan (\tan ^{-1}x)=x \\ \Rightarrow\tan (\frac{x}{\tan })=x \\ \frac{\tan }{\tan }x=x \\ x=x \end{gathered}[/tex]
