Q-if-x-1-x-2cos-prove-it-x-n-1-x-n-2cos-n-

Question Number 191610 by mehdee42 last updated on 27/Apr/23

Q : i f x + \frac{1}{x} = 2 c o s (θ) p r o v e i t x^{n} + \frac{1}{x^{n}} = 2 c o s (n θ)

Answered by Frix last updated on 27/Apr/23

z + \frac{1}{z} = 2 c \Rightarrow z = c \pm \sqrt{c^{2} - 1} \Rightarrow

x = \cos θ \pm i \sin θ = e^{\pm i θ}

x^{n} + \frac{1}{x^{n}} = e^{\pm i n θ} + e^{\mp i n θ} = 2 \cos n θ

Commented by mehdee42 last updated on 27/Apr/23

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