AP EAMCET · Maths · Inverse Trigonometric Functions
If \(\operatorname{Tanh}^{-1} \mathrm{x}=\operatorname{Coth}^{-1} \mathrm{y}=\log \sqrt{5}\), then \(\operatorname{Tan}^{-1}(\mathrm{xy})=\)
- A \(\frac{\pi}{4}\)
- B \(\frac{\pi}{3}\)
- C \(\frac{\pi}{6}\)
- D \(\frac{3 \pi}{4}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{4}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{x}=\operatorname{Tanh}(\log \sqrt{5}) = \frac{\mathrm{e}^{\log\sqrt{5}}-\mathrm{e}^{-\log\sqrt{5}}}{\mathrm{e}^{\log\sqrt{5}}+\mathrm{e}^{-\log\sqrt{5}}} = \frac{\sqrt{5}-1/\sqrt{5}}{\sqrt{5}+1/\sqrt{5}} = \frac{5-1}{5+1} = \frac{4}{6} = \frac{2}{3}\)…
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