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O-LevelAdditional MathematicsTrigonometry4037/22 · Oct/Nov 2021 · Q38 Marks

Show that (1/(secx-1)) + (1/(secx+1)) = 2 cotx cosecx.

  1. (a)Show that (1/(secx-1)) + (1/(secx+1)) = 2 cotx cosecx.[4]
  2. (b)Hence solve the equation (1/(secx-1)) + (1/(secx+1)) = 3 secx for 0° < x < 360°.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

  1. [M1]
  2. [A1]
  3. [A1]
  4. [A1] Fully correct justification of given answer: 2cotxcosecx
  5. [B1] 3tan²x = 2 oe or better, soi or 5cos²x = 3 oe or better, soi or 5sin²x = 2 oe or better, soi
  6. [M1] FT an equation of the form a tan²x = b, a > 0, b > 0 or p sin²x = q or p cos²x = q where p > 0, q > 0 and p > q
  7. [A2] no extras in range
  8. [A1] for any two correct answers

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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 2021 Paper 2 Variant 2, question 3.

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