A-LevelMathematicsTrigonometry9709/12 · Oct/Nov 2015 · Q47 Marks
Prove the identity `(1/(sin x) - 1/(tan x))² = (1 - cos x) / (1 + cos x)`
- (i)Prove the identity `(1/(sin x) - 1/(tan x))² = (1 - cos x) / (1 + cos x)`[4]
- (ii)Hence solve the equation `(1/(sin x) - 1/(tan x))² = 2/5` for `0 ≤ x ≤ 2π`.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2015). The mark or mark type is shown in brackets.
- [M1] Use of tan = sin/cos
- [M1] Use of s² = 1 - c²
- [A1] (1-c)² / ((1-c)(1+c)) OR (1-c)(1-c) / ((1-c)(1+c))
- [A1] (1-cos x) / (1+cos x) (ag)
- [M1] Making cos x the subject
- [A1] cos x = 3/7
- [A1] x = 1.13 or 5.16 (2π – 1st answer)
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