Prove that if y = 1/cos θ then dy/dθ = sec θ tan θ.

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

1. [M1] Use quotient or chain rule
2. [A1] Obtain given answer correctly
3. [M1] Multiply numerator and denominator of LHS by 1+sin θ
4. [M1] Use Pythagoras and express LHS in terms of sec θ and tan θ
5. [A1] Complete the proof
6. [M1] Express RHS in terms of cos θ and sin θ
7. [M1] Use Pythagoras and express RHS in terms of sin θ
8. [A1] Complete the proof
9. [M1] Express LHS in terms of secθ and tanθ
10. [M1] Multiply numerator and denominator by secθ + tanθ and use Pythagoras
11. [A1] Complete the proof
12. [B2] Use the identity and obtain integral 2 tan θ + 2 sec θ - θ
13. [M1] Use correct limits correctly in an integral containing terms a tan θ and b sec θ
14. [A1] Obtain answer 2√2 - π/4