OCR Further Pure Core 2 2022 June — Question 5

Exam BoardOCR
ModuleFurther Pure Core 2 (Further Pure Core 2)
Year2022
SessionJune
TopicHyperbolic functions
5
  1. By using the exponential definitions of \(\sinh x\) and \(\cosh x\), prove the identity \(\cosh 2 x \equiv \cosh ^ { 2 } x + \sinh ^ { 2 } x\).
  2. Hence find an expression for \(\cosh 2 x\) in terms of \(\cosh x\).
  3. Determine the solutions of the equation \(5 \cosh 2 x = 16 \cosh x + 21\), giving your answers in exact logarithmic form.
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