Question

$\log \left(3+2\sqrt{2}\right)=$

• A. $\sin {\text{h}}^{-1}\left(x\right)$
• B. $\cos {\text{h}}^{-1}\left(x\right)$
• C. $\tan {\text{h}}^{-1}\left(x\right)$
• D. ${\text{cot h}}^{-1}\left(x\right)$

Answer 1

The correct option is B

$\cos {\text{h}}^{-1}\left(x\right)$

Explanation for Correct Answer:

Evaluating the given function:

Given, $\log \left(3+2\sqrt{2}\right)=$

$$\begin{gathered} \log \left(3+2\sqrt{2}\right)=\log \left(3+\left(\sqrt{2}\times \sqrt{2}\times \sqrt{2}\right)\right)\left[\because 2=\sqrt{2}\times \sqrt{2}\right] \\ =\log \left(3+\sqrt{2\times 2\times 2}\right) \\ =\log \left(3+\sqrt{8}\right) \\ =\log \left(3+\sqrt{9-1}\right) \\ =\log \left(3+\sqrt{3^2-1}\right)\left[\because 3^2=9\right] \\ =\cos h^{-1}\left(3\right)\left[\because \cos h^{-1}\left(x\right)=x-\sqrt{x^2-1}\right] \end{gathered}$$

Hence, the correct answer is option (B).