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Grade 12 · Trigonometry
Compound & Double Angle Identities (Grade 12)
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  / 26

Answer all questions. Show all your working — marks are awarded for method as well as the final answer.

  1. 1
    Expand cos(A − B).
    (1)
  2. 2
    Expand sin(A + B).
    (1)
  3. 3
    Determine the exact value of cos 75° without a calculator.
    (3)
  4. 4
    Determine the exact value of sin 15° without a calculator.
    (3)
  5. 5
    Write down the three forms of cos 2A.
    (3)
  6. 6
    If sin θ = 3/5 and θ is acute, determine cos 2θ.
    (3)
  7. 7
    If sin θ = 3/5 and θ is acute, determine sin 2θ.
    (3)
  8. 8
    Prove that (sin 2A)/(1 + cos 2A) = tan A, and state the restriction on A.
    (5)
  9. 9
    Simplify 2 sin 15° cos 15°.
    (2)
  10. 10
    Why is sin(A + B) ≠ sin A + sin B?
    (2)
TOTAL: 26 marks
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