Lesson E8

E8 Proofs involving trigonometry Quiz: AQA Maths, Unit 5

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson E8, Proofs involving trigonometry: 20 multiple choice questions for the AQA Maths (7357), Unit 5: Trigonometry, written with Revision Ninja.

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The 20 questions

  1. What is the standard starting point for proving a trigonometric identity?

    • Graph both functions
    • Substitute one value
    • Rearrange both simultaneously
    • Transform one side

  2. What is used to disprove a claimed trigonometric identity?

    • A counterexample
    • An induction step
    • A geometric sketch
    • A contradiction proof

  3. Which statement is a trigonometric identity rather than an equation?

    • cos θ = 0
    • sin² θ + cos² θ = 1
    • sin θ = 0.5
    • tan θ = 1

  4. For what set of values must a trigonometric identity hold true?

    • Integer values only
    • Positive values only
    • All valid values
    • Specific values only

  5. Which identity is divided by cos²θ to prove sec²θ = 1 + tan²θ?

    • tanθ = sinθ / cosθ
    • sin²θ + cos²θ = 1
    • sin²θ - cos²θ = 1
    • secθ = 1 / cosθ

  6. Dividing both sides of a trigonometric equation by an expression requires what condition?

    • Integer value
    • Non-zero value
    • Constant value
    • Positive value

  7. Which expression is equivalent to sec θ - cos θ?

    • cosec θ cot θ
    • sin θ cos θ
    • cos θ tan θ
    • sin θ tan θ

  8. Simplify (1 - sin x)(1 + sin x).

    • 1 - 2 sin x
    • cos x
    • sin^2 x
    • cos^2 x

  9. Prove that (1 - cos 2x)/sin 2x simplifies to what?

    • 2 tan x
    • cot x
    • sin x
    • tan x

  10. Using cos 2A = 2 cos^2 A - 1, which expression gives cos^2 A in terms of cos 2A?

    • cos^2 A = cos 2A + 1
    • cos^2 A = 2 cos 2A - 1
    • cos^2 A = (1 + cos 2A)/2
    • cos^2 A = (1 - cos 2A)/2

  11. Simplify sin(A + B)/(cos A cos B).

    • tan A + tan B
    • tan(A + B)
    • tan A tan B
    • sin A + sin B

  12. Expand and simplify (sin x + cos x)^2.

    • 1 + sin 2x
    • 2 + sin 2x
    • 1 - sin 2x
    • 1 + cos 2x

  13. What is the fully simplified form of sin⁴x - cos⁴x?

    • 1 - cos²x
    • cos²x - sin²x
    • sin²x + cos²x
    • sin²x - cos²x

  14. If sin²θ = cos²θ, what is the correct relation between sin θ and cos θ?

    • tan θ = -1
    • sin θ = -cos θ
    • sin θ = ±cos θ
    • sin θ = cos θ

  15. Why is x = π/3 not the only solution to cos x = 0.5?

    • Cosine is unbounded
    • Cosine is periodic
    • Cosine is odd
    • Cosine is negative

  16. Which expression is equal to cos 4x in terms of sin 2x?

    • 1 - 2 sin^2 2x
    • 1 - sin^2 2x
    • sin 4x - 1
    • 2 sin^2 2x - 1

  17. If tan x = t, which expression gives sin 2x in terms of t?

    • 2t/(1 - t^2)
    • 2t
    • 2t/(1 + t^2)
    • t^2/(1 + t^2)

  18. Simplify sin theta/(1 + cos theta) + (1 + cos theta)/sin theta.

    • 2 sec theta
    • 2 cosec theta
    • cosec theta
    • 2 sin theta

  19. Simplify (cos 2x)/(cos x - sin x).

    • 1 + sin 2x
    • cos x - sin x
    • cos x + sin x
    • cos 2x + sin x

  20. What is the simplified value of (sec θ + tan θ)(sec θ - tan θ)?

    • -1
    • 1
    • 0
    • sec²θ

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