Show that cosec 2x + cot 2x = cotx.

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2018). The mark or mark type is shown in brackets.

1. [*M1] Express LHS in terms of sin 2x and cos2x and attempt to express in terms of sinx and cosx
2. [A1] Obtain correct 1 / (2 sin x cos x) + (cos² x - sin² x) / (2 sin x cos x) or equivalent
3. [DM1] Simplify as far as single terms involving x in numerator and denominator
4. [A1] Confirm cot x AG; necessary detail needed
5. [M1] Express in terms of sin π/8 and cos π/8 or sin π/8 and tan π/8
6. [A1] Obtain 2+√3
7. [B1] State ∫ sin 2x cot 2x dx
8. [B1] State ∫ cos 2x dx
9. [B1] Obtain ½ sin 2x + c