O-LevelAdditional MathematicsTrigonometry4037/11 · May/June 2025 · Q107 Marks
Given that 0 < θ < π/2, show that sinθ/√cosec²θ-1 + 1/√1+tan²θ can be written as secθ.
- (a)Given that 0 < θ < π/2, show that sinθ/√cosec²θ-1 + 1/√1+tan²θ can be written as secθ.[4]
- (b)Given that secx = α, where 3π/2 < x < 2π, find sinx in terms of α.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.
- [B1] for correct use of the trigonometry identity cosec²θ-1 = cot²θ
- [B1] sinθ/tanθ + cosθ oe
- [B1] sinθ × cosθ/sinθ + cosθ oe
- [B1] (sin²θ + cos²θ)/cosθ = 1/cosθ = secθ
- [B1] cos x = 1/α
- [M1] sin²x + (1/α)² = 1 oe
- [A1] sin x = -√(1 - 1/α²) oe
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →