Question

$\cos h^{-1}x=\log (2+\sqrt{3}),x=$________

• A. $1$
• B. $2$
• C. $3$
• D. $5$

Answer 1

The correct option is B $2$

Given that,

$\cos h^{-1}x=log(2+\sqrt{3}),x=?$

Solution:

We know that,

$\cos h^{-1}x=log(x+\sqrt{x^2-1})$

Thus, using equation $\left(1^2\right)$ to

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

$x+\sqrt{x^2-1}=2+\sqrt{3}$

Suppose that put $x=2$ and we get,

$2+\sqrt{2^2-1}=2+\sqrt{3}$

$2+\sqrt{4-1}=2+\sqrt{3}$

$2+\sqrt{3}=2+\sqrt{3}$

Hence, $x=2$ is required solution.