If cosh 2x = 199,then operatorname{coth} x = | vedclass

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(D) We know the identity $\cosh 2x = \frac{\operatorname{coth}^2 x + 1}{\operatorname{coth}^2 x - 1}$.Given $\cosh 2x = 199$,we have $\frac{\operatorn

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$\frac{10}{3 \sqrt{11}}$

Vedclass · Answer

(D) We know the identity $\cosh 2x = \frac{\operatorname{coth}^2 x + 1}{\operatorname{coth}^2 x - 1}$.Given $\cosh 2x = 199$,we have $\frac{\operatorname{coth}^2 x + 1}{\operatorname{coth}^2 x - 1} = 199$.Let $u = \operatorname{coth}^2 x$. Then $\frac{u + 1}{u - 1} = 199$.$u + 1 = 199u - 199$.$200 = 198u$.$u = \frac{200}{198} = \frac{100}{99}$.Thus,$\operatorname{coth}^2 x = \frac{100}{99}$.Taking the square root,$\operatorname{coth} x = \pm \sqrt{\frac{100}{99}} = \pm \frac{10}{3 \sqrt{11}}$.Considering the positive value,the result is $\frac{10}{3 \sqrt{11}}$.

If $\cosh 2x = 199$,then $\operatorname{coth} x =$

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