TS EAMCET · Maths · Inverse Trigonometric Functions
If \(\operatorname{Sinh}^{-1} x=\operatorname{Cosh}^{-1} y=\log (1+\sqrt{2})\) then \(\operatorname{Tan}^{-1}(x+y)=\)
- A \(67 \frac{1}{2}^{\circ}\)
- B \(75^{\circ}\)
- C \(22 \frac{1}{2}^{\circ}\)
- D \(15^{\circ}\)
Answer & Solution
Correct Answer
(A) \(67 \frac{1}{2}^{\circ}\)
Step-by-step Solution
Detailed explanation
\(x = \operatorname{Sinh}(\log(1+\sqrt{2})) = \frac{(1+\sqrt{2}) - \frac{1}{1+\sqrt{2}}}{2} = \frac{1+\sqrt{2} - (\sqrt{2}-1)}{2} = 1\) \(y = \operatorname{Cosh}(\log(1+\sqrt{2})) = \frac{(1+\sqrt{2}) + \frac{1}{1+\sqrt{2}}}{2} = \frac{1+\sqrt{2} + (\sqrt{2}-1)}{2} = \sqrt{2}\)…
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