TS EAMCET · Maths · Trigonometric Ratios & Identities
If \(\cosh 2 x=241\), then \(\operatorname{coth} x\) is equal to
- A \(\frac{7}{\sqrt{30}}\)
- B \(\frac{11}{\sqrt{30}}\)
- C \(\frac{7}{2 \sqrt{30}}\)
- D \(\frac{11}{2 \sqrt{30}}\)
Answer & Solution
Correct Answer
(D) \(\frac{11}{2 \sqrt{30}}\)
Step-by-step Solution
Detailed explanation
\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…
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