O-LevelAdditional MathematicsTrigonometry4037/22 · Oct/Nov 2014 · Q108 Marks
Prove that sec x cosec x - cot x = tan x.
- (i)Prove that sec x cosec x - cot x = tan x.[4]
- (ii)Use the result from part (i) to solve the equation sec x cosec x = 3 cot x for 0° < x < 360°.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2014). The mark or mark type is shown in brackets.
- [B1] (i) secxcosecx = 1 / (cosxsinx). anywhere
- [B1] (i) cotx = cosx/sinx. anywhere
- [B1ft] (i) LHS = (1-cos²x) / (cosxsinx) oe. correct addition of their terms
- [B1] (i) = sin²x / (cosxsinx) = tanx AG. use of identity and cancel
- [M1] (ii) 2cotx = tanx. equate and collect like terms, allow sign errors
- [A1] (ii) tan²x = 2 oe
- [A1] (ii) x = 54.7, 125.3, 234.7, 305.3. 2 values
- [A1] (ii) only 2 more values. awrt
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