By first expressing the equation cot θ – cot(θ + 45°) = 3 as a quadratic equation in tan θ, solve the equation for 0° < θ < 180°.

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

1. [M1] Use correct trig formula and obtain an equation in tan θ
2. [A1] Obtain a correct horizontal equation in any form e.g. 1 + tan θ – tan θ(1 – tan θ) = 3 tan θ(1 + tan θ)
3. [A1] Reduce to 2tan²θ + 3tanθ – 1 = 0 or 3-term equivalent
4. [M1] Solve 3-term quadratic and find a value of θ
5. [A1] Obtain answer 15.7°
6. [A1] Obtain answer 119.(3)°