A-LevelMathematicsTrigonometry9709/33 · May/June 2021 · Q57 Marks
By first expanding tan(2θ + 2θ), show that the equation tan 4θ = ½ tan θ may be expressed as tan⁴θ + 2 tan²θ – 7 = 0.
- (a)By first expanding tan(2θ + 2θ), show that the equation tan 4θ = ½ tan θ may be expressed as tan⁴θ + 2 tan²θ – 7 = 0.[4]
- (b)Hence solve the equation tan 4θ = ½ tan θ, for 0° < θ < 180°.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [M1] Use double angle formula to express tan 4θ in terms of tan 2θ
- [M1] Use double angle formula to express result in terms of tan θ
- [A1] Obtain a correct equation in tan θ in any form
- [A1] Obtain the given answer
- [M1] Solve for tan θ and obtain a value of θ
- [A1] Obtain answer, e.g. 53.5°
- [A1] Obtain second answer, e.g. 126.5° and no other in the interval
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