Question:
Evaluate:
\[
\cosh^{-1} 2
\]
Evaluate:
\[
\cosh^{-1} 2
\]
Show Hint
For \( \cosh^{-1} x \), use \( \cosh^{-1} x = \log (x + \sqrt{x^2 - 1}) \).
Updated On: May 21, 2025
- \( \log(2 + \sqrt{3}) \)
- \( \log(2 + \sqrt{5}) \)
- \( \log(2 - \sqrt{5}) \)
- \( \log(2 + \sqrt{2}) \)
Show Solution
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The Correct Option is A
Solution and Explanation
The formula for inverse hyperbolic cosine is:
\[
\cosh^{-1} x = \log \left( x + \sqrt{x^2 - 1} \right)
\]
Substituting \( x = 2 \):
\[
\cosh^{-1} 2 = \log \left( 2 + \sqrt{2^2 - 1} \right)
\]
\[
= \log (2 + \sqrt{4 - 1}) = \log (2 + \sqrt{3})
\]
Thus, the correct answer is \( \log(2 + \sqrt{3}) \).
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