O-LevelAdditional MathematicsTrigonometry4037/21 · May/June 2019 · Q119 Marks
Show that (cosec θ - cot θ) / sin θ = 1 / (1 + cos θ)
- (a)(i)Show that (cosec θ - cot θ) / sin θ = 1 / (1 + cos θ)[4]
- (a)(ii)Hence solve (cosec θ - cot θ) / sin θ = 5/2 for 180° < θ < 360°.[2]
- (b)Solve tan(3φ - 4) = -1/2 for 0 < φ ≤ π/2 radians.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.
- [M2] 1/sinθ - cosθ/sinθ / sinθ (M1 for either cosecθ - cotθ = 1/sinθ - cosθ/sinθ or cosecθ - cotθ / sinθ = (1/sinθ - cotθ)/sinθ or cosecθ - cotθ / sinθ = cosecθ/sinθ - cotθ/sinθ )
- [M1] (1-cosθ)/sin²θ or (1-cosθ)/(1-cos²θ)
- [A1] (1-cosθ) / ((1-cosθ)(1+cosθ)) = 1 / (1+cosθ)
- [B2] awrt 233.1 (with no extras in range) (B1 for cos θ = -3/5 soi)
- [M1] 3φ-4 = tan⁻¹(-1/2) soi
- [A2] awrt 0.132, 1.18 (with no extras in range, A1 for one correct)
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