Lesson 1.05l

1.05l Further trigonometric identities Quiz: OCR Maths, Unit 5

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 1.05l, Further trigonometric identities: 20 multiple choice questions for the OCR Maths (H240), Unit 5: Trigonometry, written with Revision Ninja.

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The 20 questions

  1. Which expression is equal to sin(A + B)?

    • cos A cos B - sin A sin B
    • sin A cos B - cos A sin B
    • cos A cos B + sin A sin B
    • sin A cos B + cos A sin B

  2. Which expression is equal to cos 2A?

    • sin^2 A - cos^2 A
    • cos^2 A - sin^2 A
    • cos^2 A + sin^2 A
    • 2 sin A cos A

  3. Which expression is equal to tan 2A?

    • 2 tan A / (1 + tan^2 A)
    • tan^2 A / (1 - 2 tan A)
    • 2 tan A / (1 - tan^2 A)
    • (tan A + tan A) / (1 + tan A)

  4. What is the exact value of 2 sin 15 cos 15 (degrees)?

    • 1/2
    • 1/4
    • sqrt(3)/2
    • sqrt(2)/2

  5. Which expression is equal to sin 2A?

    • sin^2 A - cos^2 A
    • sin A + cos A
    • 2 sin A / cos A
    • 2 sin A cos A

  6. Given sin A = 3/5 with A acute, what is cos 2A?

    • 24/25
    • 7/25
    • -7/25
    • 1/5

  7. Find the exact value of cos 75 degrees using cos(45 + 30).

    • (sqrt(6) - sqrt(2))/4
    • (sqrt(2) - sqrt(6))/4
    • (sqrt(6) + sqrt(2))/4
    • (sqrt(3) - 1)/2

  8. Using sin(2A + A), which expression equals sin 3A in terms of sin A?

    • 3 sin A - sin^3 A
    • 3 sin A - 4 sin^3 A
    • 4 sin A - 3 sin^3 A
    • 3 sin A + 4 sin^3 A

  9. Simplify sin 2x / (1 + cos 2x).

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

  10. Find the exact value of sin 75 cos 15 + cos 75 sin 15 (degrees).

    • 1/2
    • sqrt(3)/2
    • 0
    • 1

  11. Given tan A = 1/2 and tan B = 1/3, find tan(A + B).

    • 6/5
    • 1
    • 1/6
    • 5/6

  12. If tan A = 2, what is the exact value of cos 2A?

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

  13. Given cos A = 1/3 with A acute, find sin 2A.

    • 2/9
    • 8/9
    • 2 sqrt(2)/9
    • 4 sqrt(2)/9

  14. If cos 2x = 1/4, what is the value of cos^2 x?

    • 5/4
    • 3/8
    • 1/8
    • 5/8

  15. Which expression is equal to cos(A + B) cos(A - B)?

    • sin^2 A - sin^2 B
    • cos^2 A + sin^2 B
    • cos^2 A - cos^2 B
    • cos^2 A - sin^2 B

  16. Given sin A = 3/5 and cos B = 5/13 with A and B acute, find sin(A + B).

    • 63/65
    • 16/65
    • 56/65
    • 33/65

  17. Find the exact value of tan 75 degrees.

    • sqrt(3) + 1
    • 2 + sqrt(3)
    • 2 - sqrt(3)
    • 4 + sqrt(3)

  18. What is the value of the integral of cos^2 x from 0 to pi/2?

    • pi
    • pi/4
    • pi/2
    • pi/8

  19. Using a double angle formula, the exact value of sin 22.5 degrees is which expression?

    • sqrt(2 + sqrt(2))/2
    • sqrt(2 - sqrt(2))/4
    • (2 - sqrt(2))/4
    • sqrt(2 - sqrt(2))/2

  20. If cos 2 theta = -1/3, what is sin^2 theta?

    • 1/6
    • 2/3
    • 5/6
    • 1/3

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