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TS EAMCET · Maths · Inverse Trigonometric Functions

\(\sin \mathrm{h}^{-1}\left(2^{3 / 2}\right)\) is equal to :

  1. A \(\log (3+\sqrt{8})\)
  2. B \(\log (3-\sqrt{8})\)
  3. C \(\log (2+\sqrt{18})\)
  4. D \(\log (\sqrt{8}+\sqrt{27})\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\log (3+\sqrt{8})\)

Step-by-step Solution

Detailed explanation

We have \(\sin h^{-1} x=\log \left\{x+\sqrt{x^2+1}\right\}\) \(\sin h^{-1}(2)^{3 / 2}=\log \left\{2^{3 / 2}+\sqrt{\left(2^{3 / 2}\right)^2+1}\right\}\) \(=\log \{\sqrt{8}+\sqrt{8+1}\}=\log \{3+\sqrt{8}\}\)