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AP EAMCET · Maths · Trigonometric Ratios & Identities

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

  1. A \(\frac{5}{3 \sqrt{11}}\)
  2. B \(\frac{5}{6 \sqrt{11}}\)
  3. C \(\frac{7}{3 \sqrt{11}}\)
  4. D \(\frac{10}{3 \sqrt{11}}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{10}{3 \sqrt{11}}\)

Step-by-step Solution

Detailed explanation

\( \operatorname{coth}^2 x = \frac{\cosh 2x + 1}{\cosh 2x - 1} = \frac{199 + 1}{199 - 1} = \frac{200}{198} = \frac{100}{99} \) \( \operatorname{coth} x = \sqrt{\frac{100}{99}} = \frac{10}{\sqrt{99}} = \frac{10}{3 \sqrt{11}} \)