A-LevelMathematicsTrigonometry9709/32 · Oct/Nov 2024 · Q76 Marks
Show that the equation tan³x+2 tan2x-tanx = 0 may be expressed as tan⁴x-2 tan²x-3 = 0 for tanx ≠ 0.
- (a)Show that the equation tan³x+2 tan2x-tanx = 0 may be expressed as tan⁴x-2 tan²x-3 = 0 for tanx ≠ 0.[3]
- (b)Hence solve the equation tan³2θ+2 tan 4θ - tan 2θ = 0 for 0 < θ < π. Give your answers in exact form.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.
- [M1] Use correct double angle formula to obtain an equation in tan x
- [A1] Obtain a correct equation in tan x in any form without fractions
- [A1] Reduce to the given answer of tan⁴x-2tan²x-3=0 correctly
- [M1] A complete correct method to solve the equation to obtain a value for θ
- [A1] Obtain two of (θ =) π/6, π/3, 2π/3, 5π/6 and no others in the interval
- [A1] Obtain the other two of (θ =) π/6, π/3, 2π/3, 5π/6 and no others in the interval
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