Question

If $\cosh 2x=199$, then $\coth x$ equals

• A. $\frac{5}{3\sqrt{11}}$
• B. $\frac{5}{6\sqrt{11}}$
• C. $\frac{7}{3\sqrt{11}}$
• D. $\frac{10}{3\sqrt{11}}$

Answer 1

Answer: (D)

We have,
$\cosh 2x=199$
$\Rightarrow \frac{1+{\tanh }^{2}x}{1-{\tanh }^{2}x}=199$
$\Rightarrow 1+{\tanh }^{2}x=199-199{\tanh }^{2}x$
$\Rightarrow 200{\tanh }^{2}x=198$
$\Rightarrow {\tanh }^{2}x=\frac{198}{200}\Rightarrow {\tanh }^{2}x=\frac{99}{100}$
$\Rightarrow \tanh x=\frac{3\sqrt{11}}{10}\Rightarrow \coth x=\frac{10}{3\sqrt{11}}$