The angles α and β lie between 0° and 180° and are such that tan(α + β) = 2 and tan α = 3 tan β.

Mark scheme

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

1. [1] Use correct tan(A+B) formula and obtain an equation in tan α and tan β (tan α + tan β) / (1 - tan α tan β) = 2
2. [1] Substitute throughout for tan α or for tan β (e.g., (3 tan β + tan β) / (1 - 3 tan²β) = 2)
3. [1] Obtain 3tan²β+2tan β−1=0 or tan²α+2tan α-3=0
4. [1] Solve a 3-term quadratic and find an angle
5. [1] Obtain answer α = 45°, β = 18.4°
6. [1] Obtain answer α = 108.4°, β = 135°