Question

Evaluate: \[ \cosh^{-1} 2 \]

• A. \( \log(2 + \sqrt{3}) \)
• B. \( \log(2 + \sqrt{5}) \)
• C. \( \log(2 - \sqrt{5}) \)
• D. \( \log(2 + \sqrt{2}) \)

Hint:

For \( \cosh^{-1} x \), use \( \cosh^{-1} x = \log (x + \sqrt{x^2 - 1}) \).

Answer 1

The Correct Option is A

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 \( \log(2 + \sqrt{3}) \).