Question 4 - A-Level Maths

Exam Board	CAIE
Module	P3 (Pure Mathematics 3)
Year	2014
Session	November
Topic	Addition & Double Angle Formulae

Show that \(\cos \left( \theta - 60 ^ { \circ } \right) + \cos \left( \theta + 60 ^ { \circ } \right) \equiv \cos \theta\).
Given that \(\frac { \cos \left( 2 x - 60 ^ { \circ } \right) + \cos \left( 2 x + 60 ^ { \circ } \right) } { \cos \left( x - 60 ^ { \circ } \right) + \cos \left( x + 60 ^ { \circ } \right) } = 3\), find the exact value of \(\cos x\).