Question

If ${\cosh }^{-1}x=\log (2+\sqrt{3})$,then $x=$

• A. $1$
• B. $2$
• C. $3$
• D. $5$

Answer 1

Answer: (B)

$2$

Formula $cos{h}^{-1}x=ln(x+\sqrt{x^2-1})$
Given $cos{h}^{-1}x=log(2+\sqrt{3})=ln(x+\sqrt{x^2-1})$
$2+\sqrt{3}=x+\sqrt{x^2-1}$
rational part equal on both sides,
$\Rightarrow x=2$