2 marksTrigonometric Functions, Identities and Equations

CAPE Pure Mathematics Unit 1 · May/June 2009 · Paper 2 · Question 4(b)(iii)

Given that A and B are acute angles such that sin A = 3/5 and cos B = 5/13.

Find, without using tables or calculators, the EXACT values of cos 2A.

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Other parts of this question

4(a)(i)Show that x = 4 cos θ + 9 sin θ.[4 marks]
4(a)(ii)By expressing x in the form r cos (θ – α), where r is positive and 0 < α < π/2, find the MAXIMUM possible value of x.[6 marks]
4(b)(i)Find, without using tables or calculators, the EXACT values of sin (A + B).[3 marks]
4(b)(ii)Find, without using tables or calculators, the EXACT values of cos (A - B).[3 marks]
4(c)Prove that tan (x/2 + π/4) = sec x + tan x.[7 marks]

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