Solutions to this question by calculator technology are not acceptable. (a) Show that 2sin x tan x - 3 = 0 can be written as 2sin² x - 3cos x = 0.

Mark scheme

Marking points from the official mark scheme. The mark or mark type is shown in brackets.

1. Part (a): M1: For using tan x = sin x / cos x. E.g., 2sin x (sin x / cos x) - 3 = 0
2. Part (a): A1: For multiplying by cos x to obtain 2sin² x - 3cos x = 0 (must be shown).
3. Part (a): B1: (Implicit in M1 A1) for stating or using cos x ≠ 0 (e.g. at x = 90, 270)
4. Part (b): M1: For using sin² x = 1 - cos² x. E.g., 2(1 - cos² x) - 3cos x = 0
5. Part (b): A1: For correctly forming a 3-term quadratic in cos x. E.g., 2cos² x + 3cos x - 2 = 0
6. Part (b): M1: For solving the quadratic for cos x. E.g., (2cos x - 1)(cos x + 2) = 0
7. Part (b): A1: For cos x = 1/2 (and rejecting cos x = -2 as no solutions).
8. Part (b): A1: For x = 60.0° and x = 300.0° (both to 1 dp).