AP EAMCET · Maths · Inverse Trigonometric Functions
If \(\operatorname{Sinh}^{-1} x=\log 3\) and \(\operatorname{Cosh}^{-1} y=\log \frac{3}{2}\), then \(\operatorname{Tanh}^{-1}(x-y)=\)
- A \(\log \sqrt{\frac{5}{3}}\)
- B \(\log \frac{5}{3}\)
- C \(\log \frac{4}{3}\)
- D \(\log \frac{2}{\sqrt{3}}\)
Answer & Solution
Correct Answer
(A) \(\log \sqrt{\frac{5}{3}}\)
Step-by-step Solution
Detailed explanation
\( x = \operatorname{Sinh}(\log 3) \) \( x = \frac{e^{\log 3} - e^{-\log 3}}{2} = \frac{3 - \frac{1}{3}}{2} = \frac{\frac{8}{3}}{2} = \frac{4}{3} \) \( y = \operatorname{Cosh}(\log \frac{3}{2}) \)…
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