Question

If \( \sinh x = \frac{5}{12} \), then \( \cosh \frac{x}{2} \) is:

• A. \( \frac{3}{2\sqrt{5}} \)
• B. \( \frac{2}{3\sqrt{3}} \)
• C. \( \frac{5}{\sqrt{6}} \)
• D. \( \frac{5}{2\sqrt{6}} \)

Hint:

Use the identity \( \cosh^2 \frac{x}{2} = \frac{\cosh x + 1}{2} \) to simplify the calculation of \( \cosh \frac{x}{2} \).

Answer 1

The Correct Option is D

We are given \( \sinh x = \frac{5}{12} \). Using the identity for \( \cosh \frac{x}{2} \), we can solve for the value of \( \cosh \frac{x}{2} \) and find that it is \( \frac{5}{2\sqrt{6}} \).