Solve the equation 3 cotx-4 cot2x = 3 for 0° ≤ x ≤ 180°.

Mark scheme

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

1. [M1] Use correct trigonometric formulae to form an equation in tanx only, or an equation in terms of sinx and cosx only
2. [A1] Obtain a correct horizontal equation, in tanx or in cosx and sinx, in any form E.g. 3-(2 – 2 tan^2x) = 3 tanx or 2 sin^2x - 3 sinxcosx + cos^2x = 0.
3. [A1] Reduce equation to a 3-term quadratic E.g. 2 tan^2x – 3 tanx + 1 = 0, 2 sin^2x – 3 sinxcosx + cos^2x = 0. Allow if they leave the equation as a cubic with a factor of tanx and go on to give the correct solutions to the quadratic.
4. [DM1] Solve a 3-term quadratic to obtain a value for x The quadratic could be arrived at from a correct cubic Not available if they have an incorrect cubic with an incorrect quadratic factor.
5. [A1] Obtain one answer, e.g. (x =) 45°
6. [A1] Obtain a second answer, e.g. AWRT (x =) 26.6° and no other in the given interval, e.g. x = 0