Question 9 - A-Level Maths

Exam Board	CAIE
Module	P3 (Pure Mathematics 3)
Year	2011
Session	June
Topic	Addition & Double Angle Formulae

Prove the identity \(\cos 4 \theta + 4 \cos 2 \theta \equiv 8 \cos ^ { 4 } \theta - 3\).
Hence
(a) solve the equation \(\cos 4 \theta + 4 \cos 2 \theta = 1\) for \(- \frac { 1 } { 2 } \pi \leqslant \theta \leqslant \frac { 1 } { 2 } \pi\),
(b) find the exact value of \(\int _ { 0 } ^ { \frac { 1 } { 4 } \pi } \cos ^ { 4 } \theta \mathrm {~d} \theta\).