Show that 2 cosec 2θ cot θ = cosec² θ.

Mark scheme

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

1. [B1] State or imply cosec 2θ = 1/(2 sin θ cos θ)
2. [M1] Attempt to express left-hand side in terms of sine and cosine only
3. [A1] Simplify to confirm cosec² θ
4. [M1] Use identity to express left-hand side in terms of sin 30 or cosec 30
5. [A1] Obtain 2/sin 30 or 2 cosec 30 and confirm 4
6. [*M1] Solve quadratic equation of the form kcosec² (φ/2) + cosec (φ/2) - 12 = 0 or ksin² (φ/2) - sin (φ/2) - 12 = 0
7. [A1] 12sin² (φ/2) - sin (φ/2) - k = 0 correctly for cosec (φ/2) or sin (φ/2) to find two values of sin (φ/2) or cosec (φ/2)
8. [DM1] Use correct process to find at least one correct value of φ from sin(φ/2) = ±1/4, ±1/3
9. [A1] Obtain any two of -331.0, -29.0, 38.9, 321.1
10. [A1] Obtain all four values and no others between -360 and 360