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TS EAMCET · Maths · Inverse Trigonometric Functions

\(x=\log \left(\frac{1}{y}+\sqrt{1+\frac{1}{y^2}}\right) \Rightarrow y\) is equal to

  1. A \(\tanh x\)
  2. B \(\operatorname{coth} x\)
  3. C \(\operatorname{sech} x\)
  4. D \(\operatorname{cosech} x\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\operatorname{cosech} x\)

Step-by-step Solution

Detailed explanation

Given, \(x=\log \left(\frac{1}{y}+\sqrt{1+\frac{1}{y^2}}\right)\) \(\begin{array}{ll}\therefore & x=\operatorname{cosech}^{-1} y \\ \Rightarrow & y=\operatorname{cosech} x\end{array}\)