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(c) (i) Use De Moivre's theorem to show that, if sin 0+0, then (coto+i)2n+¹-(coto-i)²+1_sin (2n+1), where n is a positive integer. 21 sin 2n+10 (ii) Deduce that the solutions to the equation (2¹+¹)x² - (²x + ¹) x^-¹ + (²x + ¹) x^² + (-1)" = 0 3 5 are x=cot2 mi 2n+1, m = 1,2,3,..., n. (iii) Hence find an expression for cot² ma 2n+1, m=1 cot² (7) + cot² (27)++ ct² (7) 40. 2π 87 +...+cot² = 17 17 and show that

(c) (i) Use De Moivre's theorem to show that, if sin 0+0, then (coto+i)2n+¹-(coto-i)²+1_sin (2n+1), where n is a positive integer. 21 sin 2n+10 (ii) Deduce that the solutions to the equation (2¹+¹)x² - (²x + ¹) x^-¹ + (²x + ¹) x^² + (-1)" = 0 3 5 are x=cot2 mi 2n+1, m = 1,2,3,..., n. (iii) Hence find an expression for cot² ma 2n+1, m=1 cot² (7) + cot² (27)++ ct² (7) 40. 2π 87 +...+cot² = 17 17 and show that

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.4: Multiple-angle Formulas
Problem 41E
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(c) (i) Use De Moivre's theorem to show that, if sin 0+0, then (coto+i)2n+¹-(coto-i)²+1_sin (2n+1), where n is a positive integer. 21 sin 2n+10 (ii) Deduce that the solutions to the equation (2¹+¹)x" - (2+¹) x^-¹ +(2+¹)x^-+-+1)* = 0 3 5 are x=cot2 mi 2n+1, ,m=1,2,3,..., n. (iii) Hence find an expression for cot² mi 2n+1, 87 cot² (7) - co² (27)++ ct²() - 40. +cot2 +...+ cot2 = 17 17 m=1 and show that
Transcribed Image Text:(c) (i) Use De Moivre's theorem to show that, if sin 0+0, then (coto+i)2n+¹-(coto-i)²+1_sin (2n+1), where n is a positive integer. 21 sin 2n+10 (ii) Deduce that the solutions to the equation (2¹+¹)x" - (2+¹) x^-¹ +(2+¹)x^-+-+1)* = 0 3 5 are x=cot2 mi 2n+1, ,m=1,2,3,..., n. (iii) Hence find an expression for cot² mi 2n+1, 87 cot² (7) - co² (27)++ ct²() - 40. +cot2 +...+ cot2 = 17 17 m=1 and show that
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