(D) We know that $\cosh 2x = \frac{1 + \tanh^2 x}{1 - \tanh^2 x}$.Given $\cosh 2x = 241$,we have:$\frac{1 + \tanh^2 x}{1 - \tanh^2 x} = 241$$1 + \tanh

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(D) We know that $\cosh 2x = \frac{1 + \tanh^2 x}{1 - \tanh^2 x}$.Given $\cosh 2x = 241$,we have:$\frac{1 + \tanh^2 x}{1 - \tanh^2 x} = 241$$1 + \tanh^2 x = 241(1 - \tanh^2 x)$$1 + \tanh^2 x = 241 - 241 \tanh^2 x$$242 \tanh^2 x = 240$$\tanh^2 x = \frac{240}{242} = \frac{120}{121}$$\tanh x = \sqrt{\frac{120}{121}} = \frac{\sqrt{4 \times 30}}{11} = \frac{2 \sqrt{30}}{11}$Since $\operatorname{coth} x = \frac{1}{\tanh x}$,we get:$\operatorname{coth} x = \frac{11}{2 \sqrt{30}}$

Class 11 Mathematics Trigonometrical Ratios, Functions and Identities Mix Examples-Trigonometrical Ratios, Functions and Identities

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If $\cosh 2x = 241$,then $\operatorname{coth} x$ is equal to

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$\frac{7}{\sqrt{30}}$
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$\frac{11}{\sqrt{30}}$
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$\frac{7}{2 \sqrt{30}}$
D
$\frac{11}{2 \sqrt{30}}$

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