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1EDEXCEL FP2 June 2014 Q4
(a) Use de Moivre's theorem to show that cos(6theta) = 32cos^6(theta) - 48cos^4(theta) + 18cos^2(theta) - 1. (5) (b) Hence solve for 0 <= theta <= pi/2, 64cos^6(theta) - 96cos^4(theta) + 36cos^2(theta) - 3 = 0, giving your answers as exact multiples of pi. (5)
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2EDEXCEL FP2 June 2011 Q7
(a) Use de Moivre's theorem to show that sin(5theta) = 16sin^5(theta) - 20sin^3(theta) + 5sin(theta). (5) Hence, given also that sin(3theta) = 3sin(theta) - 4sin^3(theta), (b) find all the solutions of sin(5theta) = 5sin(3theta), in the interval 0 <= theta < 2pi. Give your answers to 3 decimal places. (6)
