plumiTrig identities: OCR A‑Level Maths questions
OCR A-Level Maths past-paper questions on 1.05.6 Trig identities, 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 12 questions on Trig identities, as a list
- June 2025, AS Paper 2, Q3 (6 marks): In a triangle ABC, AB = 9 cm, BC = 7 cm and AC = 4 cm. 2 (a) Show that cos CAB . [2] = 3 (b) Hence find the exact value of sin CAB. [2] (c) Find the exact area
- June 2024, Paper 3, Q4 (9 marks): - 4 (a) Show that the equation cot 2 x 9 cosec x 3 0 can be expressed in the form - = 2 + 5 sin x 9 sin x 2 0 . [3] - = (b) (i) In this question you must show d
- June 2024, AS Paper 1, Q3 (5 marks): In the triangle ABC, AB = 3, AC = 5 and angle BAC = a. 5. The area of the triangle is 2 Determine the two possible values of cos a. Give your answers in exact f
- June 2022, Paper 3, Q7 (8 marks): In this question you must show detailed reasoning. (a) Show that the equation m sec 3 cos 4 sin can be expressed in the form i + i = i 2i m tan 4 tan ( m 3 ) 0
- June 2022, AS Paper 1, Q4 (8 marks): In this question you must show detailed reasoning. Solve the following equations, for ° 0 x 360 ° . G G (a) 2 tan x 1 4 [3] + = 2 (b) 5 sin x 1 2 cos x [5] - =
- June 2022, AS Paper 2, Q7 (9 marks): A 2i + 4j C O 4i – 3j B The diagram shows the parallelogram OACB where OA 2 i 4 j and OB 4 i 3 j . = + = - 2 5 (a) Show that cos AOB . [5] = - 25 (b) Hence find
- November 2021, Paper 1, Q8 (10 marks): Functions f and g are defined for 0 x 2 by ( ) f x 2 tan x and ( ) g x sec x . G G = = r (a) (i) State the range of f. [1] (ii) State the range of g. [1] (b) (i
- November 2021, AS Paper 2, Q5 (9 marks): = 5 (a) Show that the equation 2 cos tan x x 3 1 ( cos x ) can be expressed in the form + 2 + 5 cos x 3 cos x 2 0 . [3] - = (b) In this question you must show d
- 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 2019, AS Paper 2, Q6 (7 marks): In this question you must show detailed reasoning. 2i (a) Show that the equation cos 6 tan cos + 4 = i i 2i can be expressed in the form 6 sin sin 2 0 . [2] + -
- June 2018, AS Paper 2, Q7 (8 marks): (i) Show that the equation x x x 2 sin tan cos 5 = + can be expressed in the form 2 + x x [3] 3 cos 5 cos 2 0 . - = (ii) Hence solve the equation 2 sin 2 tan 2
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