Question 6 - A-Level Maths

Exam Board	AQA
Module	Further AS Paper 1 (Further AS Paper 1)
Session	Specimen
Marks	12
Topic	Hyperbolic functions

Use the definitions of \(\sinh x\) and \(\cosh x\) in terms of \(\mathrm { e } ^ { x }\) and \(\mathrm { e } ^ { - x }\) to show that \(x = \frac { 1 } { 2 } \ln \left( \frac { 1 + t } { 1 - t } \right)\) where \(t = \tanh x\)
[0pt] [4 marks]
6
1. Prove \(\cosh ^ { 3 } x = \frac { 1 } { 4 } \cosh 3 x + \frac { 3 } { 4 } \cosh x\)
  [0pt] [4 marks] 6
(ii) Show that the equation \(\cosh 3 x = 13 \cosh x\) has only one positive solution.
Find this solution in exact logarithmic form.
[0pt] [4 marks]