O-LevelAdditional MathematicsTrigonometry4037/11 · May/June 2023 · Q610 Marks
6
- (a)Show that (cot θ + tan θ) / sec θ = cosec θ.[4]
- (b)Hence solve the equation ((cot(φ/3) + tan(φ/3)) / sec(φ/3))² = 2, for -540° < φ < 540°.[6]
Mark scheme
Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.
- [4] B1 for tan θ and cot θ in terms of sin and cos.
- B1 for sec θ = 1/cos θ
- M1 For dealing with the fractions in the numerator.
- A1 For correct use of cos²θ+ sin²θ = 1 to obtain the given answer.
- Alternative (2): B1 for sec θ = 1/cos θ
- M1 for dealing with the fractions in the numerator.
- (B1) For correct use of tan²θ + 1 = sec²θ
- (A1) For correct use of tan and sec² to obtain the given answer.
- [6] B2 B1 for missing
- M1 for one correct positive or negative solution of their sin(φ/3) = k
- A1 for another correct solution
- M1Dep for one negative or positive solution
- A1 for another correct solution and no extras in the range.
- -405°, -135°, 135°, 405°
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