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.

There are 4 marks available for part (i) and 4 marks for part (ii).
In total, this question is worth 11.1% of all available marks in the paper.

This is part of the set OCR A Level Problems.

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