Show that (1 + sin θ / cos θ) + (cos θ / (1 + sin θ)) = 2 sec θ.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2013). The mark or mark type is shown in brackets.

1. [M1] for dealing with the fractions, denominator must be correct, be generous with numerator
2. [DM1] for expansion and use of cos²θ + sin²θ =1
3. [DM1] for attempt to factorise
4. [A1] for obtaining final answer correctly
5. Alternative solution:
6. [M1] for dealing with the fractions
7. [DM1] for expansion and use of tan²θ +1 = sec²θ
8. [DM1] for attempt to factorise
9. [A1] for obtaining final answer correctly