Question

$\sin h^{-1}(\sin h^{-1}\theta )=$

• A. $i\theta$
• B. $\theta$
• C. $-i\theta$
• D. $\pi +i\theta$

Answer 1

The correct option is B

$\theta$

Explanation for the correct option:

Solving the given expression by using inverse trigonometric identities:

$$\begin{gathered} \sin h^{-1}\left(\sin h^{-1}\theta \right)=-i\sin \left(i\left(\sin h^{-1}\theta \right)\right)\left[\because h^{-1}=i\right] \\ =-i\sin \left(i\left(-i{\sin }^{-1}\left(i\theta \right)\right)\right) \\ =-i.i\theta \left[\because -i\sin \text{and}-i{\sin }^{-1}\text{gets cancelled}\right] \\ =\theta \end{gathered}$$

Thus, $\sin h^{-1}(\sin h^{-1}\theta )=$$\theta$

Therefore, the correct answer is option (B).