# 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.

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