Show that sinx tanx / (1-cosx) = 1+ secx.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

1. [M1] (a) LHS = sinx * (sinx/cosx) / (1-cosx) Uses tanx = sinx/cosx
2. [M1] (a) = (1 - cos²x) / (cosx(1-cosx)) Dep Uses sin²x = 1 - cos²x to eliminate sinx
3. [M1] (a) = (1 - cosx)(1 + cosx) / (cosx(1-cosx)) Dep Factorise correctly and cancel correctly.
4. [A1] (a) = 1/cosx + cosx/cosx = secx + 1 Uses 1/cosx = secx
5. [B1] (b) 5(sinx/cosx) - 3(cosx/sinx) = 2(1/cosx) Change tan x, cot x and secx into sin x and cos x correctly.
6. [M1] (b) 5sin²x - 3cos²x = 2sinx Multiply correctly by sin x cos x and use cos² x + sin² x = 1
7. [A1] (b) 8sin²x - 2sinx - 3 = 0 Three term quadratic.
8. [M1] (b) (2sinx + 1)(4sinx - 3) = 0 Factorise or use formula on their quadratic
9. [A1] (b) sinx = -1/2 → x = 210°, 330°
10. [A1] (b) sinx = 3/4 → x = 48.6°, 131.4°