CAIE P2 2010 June — Question 8

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2010
SessionJune
TopicAddition & Double Angle Formulae
8
  1. Prove the identity $$\sin \left( x - 30 ^ { \circ } \right) + \cos \left( x - 60 ^ { \circ } \right) \equiv ( \sqrt { } 3 ) \sin x$$
  2. Hence solve the equation $$\sin \left( x - 30 ^ { \circ } \right) + \cos \left( x - 60 ^ { \circ } \right) = \frac { 1 } { 2 } \sec x$$ for \(0 ^ { \circ } < x < 360 ^ { \circ }\).
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