A-LevelMathematicsTrigonometry9709/32 · Oct/Nov 2017 · Q35 Marks
By expressing the equation tan(θ + 60°) + tan(θ – 60°) = cot θ in terms of tan θ only, solve the equation for 0° < θ < 90°.
- By expressing the equation tan(θ + 60°) + tan(θ – 60°) = cot θ in terms of tan θ only, solve the equation for 0° < θ < 90°.[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.
- [1] Use correct tan(A+B) formula and express LHS in terms of tan θ
- [1] Using tan 60° = √3 and cot θ = 1/tan θ, obtain a correct equation in tan θ in any form
- [1] Reduce the equation to one in tan² θ only
- [1] Obtain 11tan² θ = 1, or equivalent
- [1] Obtain answer 16.8°
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