Solve the equation 2tan²θ+3 secθ = 18 for −180° < θ < 180°.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

1. [5] Attempt identity involving tan² θ and sec² θ to obtain quadratic equation in secθ or cos θ
2. [5] Obtain 2sec² θ+3secθ−20 = 0 or 20cos² θ−3cosθ−2=0
3. [5] Solve three-term quadratic equation to obtain at least one value of θ
4. [5] Obtain at least two values of ±66.4 and ±104.5
5. [5] Obtain all four values and no others between −180 and 180