Compound and double angle formulae: Edexcel A‑Level Maths questions

Edexcel A-Level Maths past-paper questions on 5.7 Compound and double angle formulae, 2010–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.

All 14 questions on Compound and double angle formulae, as a list

June 2025, Pure 1, Q14 (7 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. (a) Show that sin(x + 30°) + 3 cos(x +
June 2024, Pure 1, Q13 (8 marks): (a) Given that a is a positive constant, use the substitution x = a sin 2 θ to show that 1 2 2 2 2 0 0 1 d sin 2 d 2 π a x a x x a θ θ (4) (b) Hence use algebra
June 2023, Pure 2, Q14 (7 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Show that the equation 2
June 2023, Pure 2, Q15 (3 marks): A student attempts to answer the following question: Given that x is an obtuse angle, use algebra to prove by contradiction that sin x – cos x  1 The student s
June 2022, Pure 1, Q14 (8 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Given that 2 sin (x − 60°
June 2022, Pure 1, Q16 (9 marks): y 4 C R x O Figure 6 Figure 6 shows a sketch of the curve C with parametric equations x = 8 sin2 t y = 2 sin 2t + 3 sin t 0  t  π 2 The region R, shown shaded
November 2021, Pure 1, Q10 (8 marks): In this question you should show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Given that 1 + cos 2θ +
November 2020, Pure 2, Q10 (8 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Show that cos 3 A ≡ 4 cos
June 2019, Pure 1, Q6 (8 marks): (a) Solve, for –180° - ș - 180°, the equation 5 sin 2ș= 9 tan ș giving your answers, where necessary, to one decimal place. [6ROXWLRQVEDVHGHQWLUHO\RQJUDSKL
June 2019, Pure 2, Q12 (7 marks): (a) Prove cos3 sin θ θ + sin3 cos θ θ {௘FRWș ș z (90n)°, n ] (4) (b) Hence solve, for 90° ș 180°, the equation cos3 sin θ θ + sin3 cos θ θ = 4 giving any
June 2018, Pure 1, Q5 (5 marks): Given that 3sin 2sin 2cos θ y θ θ = + 3 4 4 π π θ − < < show that d d 1 sin 2 y A θ θ = + 3 4 4 π π θ − < < where A is a rational constant to be found. (5)
June 2018, Pure 1, Q14 (10 marks): A curve C has parametric equations x = 3 + 2 sin t, y = 4 + 2 cos 2t, 0  t < 2π (a) Show that all points on C satisfy y = 6 − (x − 3)2 (2) (b) (i) Sketch the c
June 2018, Pure 2, Q7 (9 marks): (i) Solve, for 0  x < 2 π , the equation 4 sin x = sec x (4) (ii) Solve, for 0  θ < 360°, the equation 5 sin θ − 5 cos θ = 2 giving your answers to one decima
June 2018, Pure 2, Q12 (9 marks): (a) Prove that 1 − cos 2θ ≡ tan θ sin 2θ, θ ≠ (2 1) 2 n π + , n ∈  (3) (b) Hence solve, for −2 π < x < 2 π , the equation (sec2 x − 5)(1 − cos 2x) = 3 tan2 x s

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