Show that 4 sin(θ + ¼π) cos(θ – ¼π) = √3 + 2 sin 2θ.

Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

1. 6(a)
2. [B1] Obtain at least either (½sinθ + ½√3cosθ) or (½cosθ + ½√3sinθ)
3. [M1] Expand and simplify with correct use of sin² θ + cos² θ =1
4. [M1] Use sinθcosθ = ½sin2θ
5. [A1] Confirm given result √3+2sin2θ AG necessary detail required.
6. 6(b)
7. [*B1] Identify value of θ is π/6
8. [DB1] Obtain √3+2sin(π/6) and conclude √3+√2
9. 6(c)
10. [B1] Identify integrand as √3 +2 sin4x
11. [M1] Integrate to obtain form k₁x + k₂ cos 4x
12. [A1] Obtain correct √3x-½cos4x
13. [A1] Obtain π√3/8 + ½