Question 4 - A-Level Maths

Exam Board	CAIE
Module	P2 (Pure Mathematics 2)
Year	2016
Session	June
Topic	Addition & Double Angle Formulae

Show that \(\sin \left( \theta + 60 ^ { \circ } \right) + \sin \left( \theta + 120 ^ { \circ } \right) \equiv ( \sqrt { } 3 ) \cos \theta\).
Hence
(a) find the exact value of \(\sin 105 ^ { \circ } + \sin 165 ^ { \circ }\),
(b) solve the equation \(\sin \left( \theta + 60 ^ { \circ } \right) + \sin \left( \theta + 120 ^ { \circ } \right) = \sec \theta\) for \(0 ^ { \circ } \leqslant \theta \leqslant 180 ^ { \circ }\).