CAPE Pure Mathematics Unit 1 · May/June 2026 · Paper 2 · Question 3(b)(i)
Derive the identity for cos 2θ in terms of cos θ only.
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- 3(a)Show that 1 + tan² θ = sec² θ.[3 marks]
- 3(b)(ii)Hence, solve cos 2θ - 3 cos θ = 1 for 0 ≤ θ ≤ 2π.[6 marks]
- 3(c)Determine the equation of the circle that has (1, 0) and (3, 2) as endpoints of a diameter.[5 marks]
- 3(d)Determine the points of intersection of the curves 2x² - y - 11 = 0 and x² - 4x - y + 10 = 0.[8 marks]
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