Question

If $x=\log (y+\sqrt{y^2+1})$, then $y=$

• A. $\tan hx$
• B. $\cot hx$
• C. $\sin hx$
• D. $\cos hx$

Answer 1

The correct option is C

$\sin hx$

Explanation for the correct option.

We know that, $\mathit{s}\mathit{i}\mathit{n}\mathbf{}{\mathit{h}}^{\mathbf{-}\mathbf{1}}\mathit{x}\mathbf{=}\mathit{l}\mathit{o}\mathit{g}\mathbf{}\left(x+\sqrt{x^2+1}\right)$

So,

$\begin{array}{rcl}\sin h^{-1}y& =& \log \left(y+\sqrt{y^2+1}\right)\\ & \Rightarrow & \sin h^{-1}y=x\\ \Rightarrow \sin hx& =& y\end{array}$

Hence, option C is correct.