# Intriguing Trigonometry Question

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It's a Paper 1 question that means no calculator. Here it goes:

sin(4x) = sin(x), 0 < x < pi.

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Interesting . . . you have to use De Moivre's theorem to figure this out, I'll give it a shot and post my answer here.

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LOL De moivre????!?!?

sin4X - sinX =0

=> sin 4x = sin x

=> 4x = kπ + (-1)^k * x

k = 0 => x = 0

k = 1 => x = π/5

k =2 => x = 2π/3

k = 3 => x = 3π/5

k = 4 => x = 4π/3

k = 5 => x = π

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I didn't try to work it out, but normally in these kind of questions they expect you to use all the rules and formula related to sine and cosine...etc..etc.

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or alternatively,

sin4x=sinx

sin4x-sinx=0

using factor formula,

sin4x-sinx= 2cos5/2xsin3/2x

2cos2.5xsin1.5x=0

cos2.5x=0

or sin1.5x=0

solve

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using factor formula,

sin4x-sinx= 2cos5/2xsin3/2x

That factor formula is nice!!

Edited by Gene-Peer

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