Q66 / 160 · TS EAMCET 2021 (06 Aug Shift 1) · Mathematics

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

  • A
    $\frac{7}{\sqrt{30}}$
  • B
    $\frac{11}{\sqrt{30}}$
  • C
    $\frac{7}{2 \sqrt{30}}$
  • Correct answer
    D
    $\frac{11}{2 \sqrt{30}}$

Solution

$\begin{aligned} & \text { We have, } \cosh 2 x=241 \\ & \Rightarrow \frac{1+\tanh ^2 x}{1-\tanh ^2 x}=241 \\ & \Rightarrow 1+\tanh ^2 x=241-241 \tanh ^2 x \\ & \Rightarrow 242 \tanh ^2 x=240 \Rightarrow \tanh ^2 x=\frac{240}{242}=\frac{120}{121} \\ & \Rightarrow \tanh x=\frac{2 \sqrt{30}}{11} \Rightarrow \operatorname{coth} x=\frac{11}{2 \sqrt{30}}\end{aligned}$

Hence, the correct answer is option: 'D'.

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