plumiCompound and double angle formulae: OCR A‑Level Maths questions
OCR A-Level Maths past-paper questions on 1.05.7 Compound and double angle formulae, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 13 questions on Compound and double angle formulae, as a list
- June 2025, Paper 2, Q4 (6 marks): / 4 (a) Prove that ( cos sin ) 1 sin 2 . [2] + + i i i cos sin + i i (b) Hence or otherwise prove that sec 2 tan 2 . [4] + i i / cos sin i - i
- June 2025, Paper 3, Q6 (12 marks): The compound angle formulae for sin A ( B ) and sin A ( B ) are + - sin ( A B ) sin A cos B cos A sin B and + = + sin ( A B ) sin A cos B cos A sin B . - = - (a
- June 2024, Paper 2, Q6 (10 marks): In this question you must show detailed reasoning. (a) (i) Use the formula for cos A ( B ) , and the double angle formulae, to show that + 3i cos 3 4 cos 3 cos
- June 2023, Paper 1, Q7 (9 marks): (a) Use the result cos ( A B ) cos A cos B sin A sin B to show that + = - cos ( A B ) cos A cos B sin A sin B . [2] - = + The function ( ) f i is defined as cos
- June 2023, Paper 3, Q5 (9 marks): A mathematics department is designing a new emblem to place on the walls outside its classrooms. The design for the emblem is shown in the diagram below. y x O
- June 2022, Paper 1, Q9 (7 marks): y 1 2 9 Use the substitution x 2 sin to show that 4 x d x . [7] = i - = r 3 1
- November 2021, Paper 1, Q10 (11 marks): (a) C x y b a A D B The diagram shows triangle ABC. The perpendicular from C to AB meets AB at D. Angle ACD = , angle x D B = C y , length BC = a and length AC
- November 2021, Paper 2, Q7 (4 marks): Differentiate cos x with respect to x, from first principles. [4]
- November 2020, Paper 1, Q11 (10 marks): In this question you must show detailed reasoning. y A P x O 2 2 The diagram shows a circle with equation x y 10 x 14 y 64 0 . A tangent is drawn from + - - + =
- November 2020, Paper 2, Q6 (3 marks): 2 6 Prove that 2 cos ( 2 45 °) cos 2 sin cos sin , where i is measured in degrees. [3] + - - i / i i i i
- June 2018, Paper 2, Q4 (4 marks): Prove that sin2(i + 45)° - cos2(i + 45)° / sin 2i °. 4 [4]
- June 2018, Paper 3, Q6 (8 marks): a k a k. 1 1 6 It is given that the angle i satisfies the equation sin 2 3 cos 2 i + r = i + r 4 4 1 (i) Show that tan2 [3] . i = 2 (ii) Hence find, in surd for
- June 2018, Paper 3, Q10 (11 marks): Three forces, of magnitudes 4 N, 6 N and P N, act at a point in the directions shown in the diagram. 6N 4N i 2i PN The forces are in equilibrium. (i) Show that
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