Showing all necessary working, solve the equation cot θ + cot(θ + 45°) = 2, for 0° < θ < 180°.

Mark scheme

Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.

1. [M1] Use correct tan (A + B) formula and obtain an equation in tan θ
2. [A1] Obtain a correct equation in any form
3. [A1] Reduce to 3 tan²θ = 1, or equivalent
4. [A1] Obtain answer x = 30°
5. [A1] Obtain answer x = 150°
6. OR: use correct sin(A+B) and cos(A+B) to form equation in sine and cos θ
7. [M1A1] Reduce to tan² θ = 1/3, sin² θ = 1/4, cos² θ = 3/4 etc.