Solve the equation 2 cot 2x + 3 cotx = 5, for 0° < x < 180°.

Mark scheme

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

1. [*M1] Use correct trigonometric formulae to form an equation in tanx e.g. 2((1-tan²x)/(2tanx)) + 3/tanx = 5
2. [A1] Obtain a correct linear equation in any form e.g. 1 - tan²x + 3 = 5 tan x
3. [A1] Reduce equation to a 3-term quadratic tan²x + 5 tan x − 4 = 0, or 3-term equivalent
4. [DM1] Solve a 3-term quadratic in tan x and obtain a value of x
5. [A1] Obtain answer, e.g. x = 35.1°
6. [A1] Obtain second answer, e.g. x = 99.9°, and no other in (0°, 180°)
7. Alternative method for question 3
8. [*M1] Use correct formulae for sin2x and cos2x to form an equation in sinx and cosx
9. [A1] Obtain 4(cosx/sinx) - (sinx/cosx) = 5
10. [A1] Reduce equation to a 3-term quadratic tan²x + 5 tan x 4 = 0, or 3-term equivalent
11. [DM1] Solve a 3-term quadratic in tan x and obtain a value of x
12. [A1] Obtain answer, e.g. x = 35.1°
13. [A1] Obtain second answer, e.g. x = 99.9°, and no other in (0°,180°)