AP EAMCET · Maths · Inverse Trigonometric Functions
If \(\operatorname{Sinh}^{-1}(2)+\operatorname{Sinh}^{-1}(3)=\alpha\) then \(\sinh \alpha=\)
- A \(2 \sqrt{5}+3 \sqrt{10}\)
- B \(2 \sqrt{10}+4 \sqrt{5}\)
- C \(3 \sqrt{10}+4 \sqrt{5}\)
- D \(2 \sqrt{10}+3 \sqrt{5}\)
Answer & Solution
Correct Answer
(D) \(2 \sqrt{10}+3 \sqrt{5}\)
Step-by-step Solution
Detailed explanation
\(\operatorname{Sinh}^{-1}(x)+\operatorname{Sinh}^{-1}(y)=\operatorname{Sinh}^{-1}(x \sqrt{1+y^2}+y \sqrt{1+x^2})\) \(\alpha = \operatorname{Sinh}^{-1}(2 \sqrt{1+3^2}+3 \sqrt{1+2^2})\) \(\sinh \alpha = 2 \sqrt{10}+3 \sqrt{5}\)
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