A-LevelMathematicsTrigonometry9709/31 · Oct/Nov 2021 · Q56 Marks
Show that the equation cot 2θ + cot θ = 2 can be expressed as a quadratic equation in tan θ.
- (a)Show that the equation cot 2θ + cot θ = 2 can be expressed as a quadratic equation in tan θ.[3]
- (b)Hence solve the equation cot 2θ + cot θ = 2, for 0 < θ <π, giving your answers correct to 3 decimal places.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.
- [M1] Use correct trig formulae and express equation in terms of tan θ
- [A1] Obtain a correct equation in tan θ in any form
- [A1] Reduce to `tan²θ + 4tanθ - 3 = 0`, or 3-term equivalent
- [M1] Solve a 3-term quadratic for tan θ and calculate θ
- [A1] Obtain answer, e.g. 0.573
- [A1] Obtain second answer, e.g. 1.783 and no other
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