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O-LevelAdditional MathematicsTrigonometry4037/22 · Oct/Nov 2018 · Q88 Marks

Show that 1/(1-sinx) - 1/(1+sinx) = 2tanxsecx.

  1. (i)Show that 1/(1-sinx) - 1/(1+sinx) = 2tanxsecx.[4]
  2. (ii)Hence solve the equation 1/(1-sinx) - 1/(1+sinx) = cosecx for 0° ≤ x ≤ 360°.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

  1. [M1] (1+sinx)-(1-sinx) / (1-sinx)(1+sinx)
  2. [A1] 2sinx / 1-sin²x
  3. [M1] 2sinx / cos²x
  4. [A1] 2sinx/cosx * 1/cosx = 2tanxsecx AG
  5. [M1] equate 2secxtanx = cosecx
  6. [A1] tan²x = 1/2
  7. [A1] two correct
  8. [A1] 35.3°, 144.7°, 215.3°, 324.7°

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About this question

Topic
Trigonometry, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2018 Paper 2 Variant 2, question 8.

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