Question 7 - A-Level Maths

Exam Board	CAIE
Module	P3 (Pure Mathematics 3)
Year	2024
Session	June
Topic	Addition & Double Angle Formulae

Show that \(\cos ^ { 4 } \theta - \sin ^ { 4 } \theta \equiv \cos 2 \theta\).
Hence find the exact value of \(\int _ { - \frac { 1 } { 8 } \pi } ^ { \frac { 1 } { 8 } \pi } \left( \cos ^ { 4 } \theta - \sin ^ { 4 } \theta + 4 \sin ^ { 2 } \theta \cos ^ { 2 } \theta \right) \mathrm { d } \theta\).