# OCR A Level: Further Pure 2 - Hyperbolics [January 2010 Q5]

**Geometry**Level pending

\((\text{i})\) Using the definitions of \(\sinh x\) and \(\cosh x\) in terms of \(e^x\) and \(e^{-x}\), show that \[\cosh^2 x - \sinh^2 x \equiv 1 . \]

\((\text{ii})\) Solve the equation \[2 \tanh^2 x - \text{sech} \, x = 1\] giving your answer(s) in logarithmic form.

**If the sum of all the solutions is \(\ln a\), input \(a\) as your answer.**