Question 13 - A-Level Maths

Exam Board	OCR MEI
Module	Further Pure Core (Further Pure Core)
Year	2020
Session	November
Topic	Hyperbolic functions

Using exponentials, prove that \(\sinh 2 x = 2 \cosh x \sinh x\).
Hence show that if \(\mathrm { f } ( x ) = \sinh ^ { 2 } x\), then \(\mathrm { f } ^ { \prime \prime } ( x ) = 2 \cosh 2 x\).
Explain why the coefficients of odd powers in the Maclaurin series for \(\sinh ^ { 2 } x\) are all zero.
Find the coefficient of \(x ^ { n }\) in this series when \(n\) is a positive even number.