O-LevelAdditional MathematicsTrigonometry4037/12 · May/June 2016 · Q57 Marks
Show that (1 - cos θ)(1 + sec θ) = sin θ tan θ.
- (i)Show that (1 - cos θ)(1 + sec θ) = sin θ tan θ.[4]
- (ii)Hence solve the equation (1 - cos θ)(1 + sec θ) = sin θ for 0 ≤ θ ≤ π radians.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.
- [1] M1 for expansion and use of secθ = 1/cosθ consistently, allow one sign error
- [1] DM1 for attempt at a single fraction, dependent on first M1
- [1] A1
- [1] A1
- [1] B1 for θ = π/4 from tanθ = 1
- [1] B1 for θ = 0 from sinθ = 0
- [1] B1 for θ = π from sinθ = 0
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