A-LevelFurther MathematicsComplex NumbersOct/Nov 2015Paper 1 Q1012 Marks
Using de Moivre's theorem, show that tan 5θ = (5 tan θ - 10 tan³ θ + tan⁵ θ) / (1 - 10 tan² θ + 5 tan⁴ θ). Hence show that the equation x² – 10x + 5 = 0 has roots tan²(π/5) and tan²(2π/5). Deduce a quadratic equation, with integer coefficients, having roots sec²(π/5) and sec²(2π/5).
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