Solve the equation 3 sin(2x+π/4) = √3 cos(2x+π/4), for 0 ≤ x ≤ π.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

1. [1] tan (2x+π/4) = 1/√3 seen or implied (must be from correct working)
2. [1] For attempt at the correct order of operations (e.g. 2x+π/4 = π/6), may be implied by x = -π/24
3. [1] For an attempt to find a second solution within the given range (e.g. 2x+π/4 = 7π/6 or 13π/6)
4. [1] x = 11π/24 or x = 23π/24 (for one correct solution)
5. [1] For a second solution x = 11π/24 and x = 23π/24 within the given range with no extra solutions within the range.