TS EAMCET · Maths · Trigonometric Ratios & Identities
If \(\cosh ^{-1} x=2 \log _e(\sqrt{2}+1)\), then \(x=\)
- A 1
- B 2
- C 4
- D 3
Answer & Solution
Correct Answer
(D) 3
Step-by-step Solution
Detailed explanation
We have, \(\cosh ^{-1} x=2 \log _e(\sqrt{2}+1)\) \[ \begin{aligned} & \Rightarrow \log _e\left(x+\sqrt{x^2-1}\right)=\log _e(\sqrt{2}+1)^2 \\ & \Rightarrow \quad x+\sqrt{x^2-1}=(\sqrt{2}+1)^2 \\ & \Rightarrow \quad x+\sqrt{x^2-1}=3+2 \sqrt{2}=3+\sqrt{8} \end{aligned} \] On…
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