Solve the equation sec² θ cot θ = 8 for 0 < θ < π.

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2021). The mark or mark type is shown in brackets.

1. [B1] State 1/cos²θ × cosθ/sinθ = 8 OE involving sinθ and cosθ only.
2. [M1] Attempt use of sin 2θ identity to obtain sin 2θ = k
3. [A1] Obtain sin 2θ = 1/4
4. [M1] Use correct process to find two values of θ between 0 and π
5. [A1] Obtain 0.126 and 1.44
6. [B1] State (1+tan²θ)/tanθ = 8
7. [M1] Attempt solution of 3-term quadratic equation to find values of tanθ
8. [A1] Obtain tanθ = (8±√60)/2 OE
9. [M1] Solve tanθ = ... to find two values of θ between 0 and π
10. [A1] Obtain 0.126 and 1.44