O-LevelAdditional MathematicsTrigonometry4037/22 · May/June 2018 · Q15 Marks
Show that cos θ cot θ + sin θ = cosec θ.
- (i)Show that cos θ cot θ + sin θ = cosec θ.[3]
- (ii)Hence solve cos θ cot θ + sin θ = 4 for 0° ≤ θ ≤ 90°.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- [B1] uses cot θ = cos θ / sin θ oe or tan θ = sin θ / cos θ oe at some stage
- [B1] uses cos² θ + sin² θ = 1 oe
- [B1] for common denominator of sin θ oe either in a compound fraction or in two partial fractions OR for writing (1 – sin² θ) / sin θ as 1 / sin θ – sin² θ / sin θ oe
- [M1] sin θ = 1/4
- [A1] 14.5° or 14.47[751...] rot to 4 or more figures isw
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