Question

Evaluate \[ \log\left(\sinh\theta+\sqrt{\sinh^2\theta+1}\right). \]

• A. \(\cosh\theta\)
• B. \(\sinh^{-1}\theta\)
• C. \(\theta\)
• D. \(\cosh^{-1}\theta\)

Hint:

Remember the standard identities \[ \boxed{\cosh^2x-\sinh^2x=1} \] and \[ \boxed{\sinh x+\cosh x=e^x.} \] These directly simplify logarithmic expressions involving hyperbolic functions.

Answer 1

The Correct Option is C