Lesson E5

E5 Trigonometric identities Quiz: AQA Maths, Unit 5

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson E5, Trigonometric identities: 20 multiple choice questions for the AQA Maths (7357), Unit 5: Trigonometry, written with Revision Ninja.

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The 20 questions

  1. Which quotient expression is equivalent to tan theta?

    • 1 / cos theta
    • sin theta / cos theta
    • 1 / sin theta
    • cos theta / sin theta

  2. Which expression is equal to sec^2 theta?

    • 1 - tan^2 theta
    • 1 + tan^2 theta
    • tan^2 theta - 1
    • 1 + cot^2 theta

  3. Which expression is equal to cosec^2 theta?

    • 1 - cot^2 theta
    • cot^2 theta - 1
    • 1 + tan^2 theta
    • 1 + cot^2 theta

  4. Simplify sin^2 x + cos^2 x.

    • tan x
    • 2
    • 1
    • 0

  5. Which expression is equivalent to 1 - cos^2 theta?

    • sin^2 theta
    • tan^2 theta
    • cos^2 theta
    • -sin^2 theta

  6. Simplify cot theta x sin theta.

    • cos theta
    • sin theta
    • 1/cos theta
    • tan theta

  7. Simplify sec theta x cos theta.

    • 0
    • tan theta
    • sin theta
    • 1

  8. Given sin theta = 3/5 with theta acute, find cos theta.

    • 4/5
    • 5/3
    • 5/4
    • 3/4

  9. Given cos theta = 5/13 with theta acute, find tan theta.

    • 12/5
    • 5/12
    • 13/12
    • 12/13

  10. Simplify sec^2 theta - tan^2 theta.

    • tan^2 theta
    • sec^2 theta
    • 1
    • 2

  11. Simplify (1 - cos^2 x)/sin x.

    • cos x
    • sin^2 x
    • sin x
    • tan x

  12. Simplify (sec^2 theta - 1) cos^2 theta.

    • 1
    • cos^2 theta
    • sin^2 theta
    • tan^2 theta

  13. Simplify (1 + tan^2 x)/(1 + cot^2 x).

    • cot^2 x
    • tan^2 x
    • sec^2 x
    • 1

  14. Given sin theta = 2/3 with cos theta negative, find cos theta.

    • -5/9
    • -sqrt(5)/3
    • sqrt(5)/3
    • -sqrt(5)/9

  15. Express sin^2 theta + 2 cos^2 theta in terms of cos theta only.

    • 1 + cos^2 theta
    • 2 cos^2 theta
    • 1 - cos^2 theta
    • 3 cos^2 theta - 1

  16. What is the single product equivalent to tan theta + cot theta?

    • sin theta cos theta
    • sec theta cosec theta
    • tan theta cot theta
    • sec theta / cosec theta

  17. Express 1/(1 - sin theta) + 1/(1 + sin theta) in terms of sec theta.

    • sec^2 theta
    • 2 sec^2 theta
    • 2 cos^2 theta
    • 2 tan^2 theta

  18. Given tan theta = 2 with theta in the first quadrant, find sin theta.

    • sqrt(5)/2
    • 2/5
    • 2/sqrt(5)
    • 1/sqrt(5)

  19. Given sec theta = 4 with theta in the fourth quadrant, find sin theta.

    • -1/4
    • -sqrt(15)/4
    • -4/sqrt(15)
    • sqrt(15)/4

  20. Simplify (sin θ + cos θ)² − 2 sin θ cos θ.

    • 2
    • 2 sin θ
    • 1
    • 0

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