Question 5 - A-Level Maths

Exam Board	CAIE
Module	P3 (Pure Mathematics 3)
Year	2009
Session	November
Topic	Standard Integrals and Reverse Chain Rule

Prove the identity $\cos 4 \theta - 4 \cos 2 \theta + 3 \equiv 8 \sin ^ { 4 } \theta$.
Using this result find, in simplified form, the exact value of $$\int _ { \frac { 1 } { 6 } \pi } ^ { \frac { 1 } { 3 } \pi } \sin ^ { 4 } \theta \mathrm {~d} \theta$$