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TS EAMCET · Maths · Functions

If \(x=\log \left(y+\sqrt{y^2+1}\right)\) then \(y=\)

  1. A \(\tan h x\)
  2. B \(\operatorname{cot h} \mathrm{x}\)
  3. C \(\sin h \mathrm{x}\)
  4. D \(\cos h x\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\sin h \mathrm{x}\)

Step-by-step Solution

Detailed explanation

\(x=\log \left(y+\sqrt{\left.y^2+1\right)}\right.\) \(\begin{aligned} & y+\sqrt{y^2+1}=e^x \\ & \because \sin h^{-1} x=\log \left(x+\sqrt{x^2+1}\right) \\ & \sin h^{-1} y=\log \left(y+\sqrt{y^2+1}\right) \\ & \sin h^{-1} y=x \Rightarrow \sin h x=y\end{aligned}\)