Solve the equation (2-3 cotx) cosx = 0 for 0 < x ≤ π/2.

Mark scheme

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

1. [M1] cos x = 0 or tan x = 3/2 oe
2. [A2] and no extra solutions in range A1 for either ignoring extras
3. [A1] [x =] π/2 or 1.57[07...]
4. [A1] 0.983 or 0.9827[93...]
5. [M1] Writes in terms of cosec(2θ+1) or sin(2θ+1) only.
6. [A1] 12sin²(2θ+1) + 5sin(2θ+1) - 2 [=0] or 2cosec²(2θ+1) - 5cosec(2θ+1) - 12 [=0] oe
7. [M1] Factorises or solves their 3-term quadratic in sin(2θ+1) or cosec(2θ+1) dep on previous M1
8. [M1] dep on previous M1 FT providing -1 < their 1/4 < 1 and/or -1 < their -2/3 < 1
9. [A2] and no extra solutions in range A1 for two correct solutions ignoring extras in range
10. [A1] -0.374 or -0.3736[59...]
11. [A1] 0.944 or 0.9444[56...]
12. [A1] -0.865 or -0.8648[63...]
13. [A1] 1.44 or 1.435[66...]