ExamBro
ExamBro
AP EAMCET · Maths · Inverse Trigonometric Functions

If \(\operatorname{sech}^{-1} \mathrm{x}=\log 2\) and \(\operatorname{cosech}^{-1} \mathrm{y}=-\log 3\), then \((\mathrm{x}+\mathrm{y})=\)

  1. A \(\frac{1}{6}\)
  2. B \(\frac{1}{20}\)
  3. C \(6\)
  4. D \(20\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{1}{20}\)

Step-by-step Solution

Detailed explanation

\(x = \operatorname{sech}(\log 2) = \frac{2}{e^{\log 2} + e^{-\log 2}} = \frac{2}{2 + \frac{1}{2}} = \frac{4}{5}\) \(y = \operatorname{cosech}(-\log 3) = \frac{2}{e^{-\log 3} - e^{\log 3}} = \frac{2}{\frac{1}{3} - 3} = -\frac{3}{4}\)…