9 marksTrigonometric Functions, Identities and Equations

CAPE Pure Mathematics Unit 1 · May/June 2023 · Paper 2 · Question 3(a)

Prove that (1 - \sin\theta)/(1 + \sin\theta) = (\sec\theta - \tan\theta)^2.

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3(b)Solve the equation 2\cos^2 x - 3\sin x = 3 for 0 \le x \le 2\pi.[9 marks]
3(c)Show that \cos(\pi/2 + x) = -\sin x.[4 marks]
3(d)A and B are acute angles such that \sin A = 3/5 and \cos B = 5/13. Calculate, without using tables or calculators, the EXACT value of \cos(A - B).[3 marks]

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