Show that sin 2θ cot θ – cos 2θ = 1.

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2022). The mark or mark type is shown in brackets.

1. [B1] Use at least two of sin 2θ = 2 sin θ cos θ, cos 2θ = cos² θ – sin² θ, cot θ = cos θ/sin θ [OE]
2. [M1] Express LHS in terms of sin θ and cos θ only and attempt valid simplification
3. [A1] Obtain cos² θ + sin² θ or equivalent and hence 1 [AG – necessary detail needed]
4. [M1] Substitute θ = π/6 and show or imply sin(π/3)cot(π/6) = 1 + cos(π/3)
5. [A1] Obtain 1 + √3 or exact equivalent
6. [M1] Use the identity from part (a) to obtain -2 cos 2θ = 0 or equivalent [Or alternative starting again, using valid simplification and reaching single trigonometric function.]
7. [A1] Obtain θ = π/4