O-LevelAdditional MathematicsTrigonometry4037/21 · May/June 2017 · Q118 Marks

Prove that sinx(cotx + tanx) = secx.

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

[B2] cosx/sinx + sinx/cosx = (cos²x + sin²x)/(sinx cosx) oe B1 for either cotx = cosx/sinx or tanx = sinx/cosx used B1 for correctly placing over a common denominator or for splitting into 3 correct terms not just for stating or working from both sides
[B1] Valid use of Pythagorean identity e.g. cos²x + sin²x = 1
[B1] Simplification to secx (correct solution only) not if working from both sides
[M1] |cosx| = 1/2 soi
[A1] 60, 300 Correct pair
[M1] cosx = -1/2 soi
[A1] 120, 240 Correct pair

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Topic: Trigonometry, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source: O-Level Additional Mathematics, May/June 2017 Paper 2 Variant 1, question 11.

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