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O-LevelAdditional MathematicsTrigonometry4037/11 · May/June 2020 · Q1012 Marks

Show that 1/(sec θ - 1) - 1/(sec θ + 1) = 2 cot² θ.

  1. (a)(i)Show that 1/(sec θ - 1) - 1/(sec θ + 1) = 2 cot² θ.[3]
  2. (a)(ii)Hence solve 1/(sec 2x - 1) - 1/(sec 2x + 1) = 6 for -90° < x < 90°.[5]
  3. (b)Solve cosec(y + π/3) = 2 for 0 ≤ y ≤ 2π radians, giving your answers in terms of π.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

  1. [M1] For dealing with the fractions
  2. [M1] For use of the correct identity
  3. [A1] Al for given answer, must see 8 / tan^2θ first
  4. [M1] M1 for use of (i) and attempt to simplify
  5. [A1] tan 2x = ± 1/√3
  6. [M1] M1 for attempt to solve, may be implied by one correct solution
  7. [A2] Al for each pair of correct solutions
  8. [M1] For dealing with cosec and an attempt to solve
  9. [M1] M1 for a complete method of solution, may be implied by a correct solution
  10. [A1] y = π/2
  11. [A1] y = 11π/6

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About this question

Topic
Trigonometry, O-Level Additional Mathematics (syllabus 4037). Structured question, 12 marks.
Source
O-Level Additional Mathematics, May/June 2020 Paper 1 Variant 1, question 10.

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