Question

If \[ \sinh x=-\frac12,\qquad \cosh y=2, \] and \[ x+y=\log p, \] then \(p=\)

• A. \(\dfrac{4+2\sqrt3}{\sqrt5+1}\)
• B. \(\dfrac{\sqrt5-1}{4\sqrt3+2}\)
• C. \((\sqrt5-1)(2+\sqrt3)\)
• D. \(\dfrac{4-2\sqrt3}{\sqrt5+1}\)

Hint:

For hyperbolic function equations, substitute \(e^x=t\) or \(e^y=t\) to obtain a quadratic equation. Then use \(e^{x+y}=e^x e^y\) whenever logarithms are involved.

Answer 1

The Correct Option is A