Let = cos 1/5 + is in 1/5 . Show that 5 + 1

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Let ω = cos 1/5 π + is in 1/5 π. Show that ω⁵ + 1 = 0 and deduce that ω⁴ – ω³ + ω² – ω = -1.

Show further that ω – ω⁴ = 2 cos 1/5 π and ω³ – ω² = 2cos 3/5 π.

Hence find the values of

Find a quadratic equation having roots cos 1/5π and cos 3/5π and deduce the exact value of cos 1/5π.

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Cambridge International AS & A Level Further Mathematics Coursebook

ISBN: 9781108403375

1st Edition

Authors: Lee Mckelvey, Martin Crozier

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Question Posted: Oct 15, 2021 01:00 AM

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Let = cos 1/5 + is in 1/5 . Show that 5 + 1

Question:

1 3 cos- + coS T and cos-TCOS T. 5 3 os A. 5 5

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First we can use De Moivres theorem to show that 5 1 0 5 cos 15 i sin 15 5 cos 1 i sin 1 using the b...View the full answer

Cambridge International AS & A Level Further Mathematics Coursebook

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