plumiTrig proofs: OCR A‑Level Maths questions
OCR A-Level Maths past-paper questions on 1.05.10 Trig proofs, 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 8 questions on Trig proofs, 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, AS Paper 1, Q4 (7 marks): cos 1 i 4 (a) Show that tan (where 90 n ° for any odd integer n). [3] - i i ! / 1 sin cos - i i cos 3 x 1 (b) Hence solve the equation = for 1 0 x 90 ° . [4] -
- June 2023, AS Paper 1, Q1 (5 marks): 1 1 (a) Prove that cos x sin x tan x (where x n r for any odd integer n). [3] + / ! cos x 2 2 2 (b) Solve the equation sin 2 x cos x for 0 x 180 c. [2] = c G G
- 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 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
- November 2020, AS Paper 1, Q3 (8 marks): In this question you must show detailed reasoning. 4sin2 2 (a) Solve the equation tan for 0 ° 180 ° . [5] i = i G i G sin2 1 cos - + i i (b) Prove that cos ( co
- June 2019, Paper 3, Q5 (9 marks): In this question you must show detailed reasoning. 1 cos + i 2 (a) Prove that ( cot cosec ) . [4] + = i i 1 cos - i 2 (b) Hence solve, for 0 1 1 2 , r ( 3 cot c
- June 2018, Paper 2, Q4 (4 marks): Prove that sin2(i + 45)° - cos2(i + 45)° / sin 2i °. 4 [4]
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