TS EAMCET · Maths · Inverse Trigonometric Functions
If \(2 \operatorname{Tanh}^{-1} x=\operatorname{Sinh}^{-1}\left(\frac{4}{3}\right)\) then \(\operatorname{Cosh}^{-1}\left(\frac{1}{x}\right)=\)
- A \(\log (\sqrt{2}+1)\)
- B \(\log (\sqrt{2}-1)\)
- C \(\log (2+\sqrt{3})\)
- D \(\log (2-\sqrt{3})\)
Answer & Solution
Correct Answer
(C) \(\log (2+\sqrt{3})\)
Step-by-step Solution
Detailed explanation
\(A = \operatorname{Sinh}^{-1}\left(\frac{4}{3}\right) \Rightarrow \operatorname{Sinh} A = \frac{4}{3}\) \(\operatorname{Cosh} A = \sqrt{1+\operatorname{Sinh}^2 A} = \sqrt{1+\left(\frac{4}{3}\right)^2} = \sqrt{1+\frac{16}{9}} = \sqrt{\frac{25}{9}} = \frac{5}{3}\)…
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