A-LevelMathematicsTrigonometry9709/32 · Oct/Nov 2020 · Q46 Marks
Show that the equation tan(θ + 60°) = 2 cot θ can be written in the form tan²θ + 3√3 tan θ – 2 = 0.
- (a)Show that the equation tan(θ + 60°) = 2 cot θ can be written in the form tan²θ + 3√3 tan θ – 2 = 0.[3]
- (b)Hence solve the equation tan(θ+ 60°) = 2 cot θ, for 0° < θ < 180°.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- [M1] Use correct tan(A+B) formula and obtain an equation in tan θ
- [A1] Use tan 60° = √3 and obtain a correct horizontal equation in any form
- [A1] Reduce to tan²θ + 3√3 tan θ – 2 = 0 correctly
- [M1] Solve the given quadratic to obtain a value for tan θ
- [A1] Obtain one correct answer e.g. θ = 19.8°
- [A1] Obtain second correct answer θ = 100.2° and no others in the given interval
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