Express 3 cos 2x - √3 sin 2x in the form Rcos(2x+α), where R > 0 and 0 < α < ½π. Give the exact values of R and α.

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

1. [B1] State R = √12 or exact equivalent
2. [M1] Use trig formula to find α
3. [A1] Obtain α = π/6 or exact equivalent
4. [B1FT] Express integral in the form A ∫ sec² (2x +...)dx or A ∫sec² (2x-...) dx
5. [B1FT] Integrate and reach B tan (2x + ...) or B tan (2x –...)
6. [B1FT] Obtain (1/8)tan (2x+...)
7. [M1] Use limits of x = 0 and x = π/12 in the correct order in expression of form B tan (π/6 + ...) - B tan(...)
8. [A1] Obtain answer √3/8 or (1/√3)/8 or 1/(4√3) or 1/√48 or single term exact equivalent