7 marksTrigonometric Functions, Identities and Equations

CAPE Pure Mathematics Unit 1 · May/June 2012 · Paper 2 · Question 3(a)(i)

Given that cos (A + B) = cos A cos B – sin A sin B and cos 2θ = 2 cos² θ-1,

prove that cos 3θ = 2 cos θ [cos² θ – sin² θ – 1/2].

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Other parts of this question

3(a)(ii)Using the appropriate formula, show that 1/2 [sin 6θ – sin 2θ] = (2 cos² 2θ – 1) sin 2θ.[5 marks]
3(a)(iii)Hence, or otherwise, solve sin 6θ − sin 2θ = 0 for 0 ≤ θ ≤ π/2.[5 marks]
3(b)Find ALL possible values of cos θ such that 2 cot² θ + cos θ = 0.[8 marks]

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