- #1

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## Homework Statement

If sin x + sin2x + sin3x= 1, then find out the value of cos6x-4cos4x+8cos2x.

## Homework Equations

## The Attempt at a Solution

How should i start?

I don't find any way to convert them to cos 6x or cos 4x.

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- Thread starter Saitama
- Start date

- #1

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- 92

If sin x + sin2x + sin3x= 1, then find out the value of cos6x-4cos4x+8cos2x.

How should i start?

I don't find any way to convert them to cos 6x or cos 4x.

- #2

SammyS

Staff Emeritus

Science Advisor

Homework Helper

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-- Just a possibility.

- #3

- 3,812

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-- Just a possibility.

Using this identity i get:-

2sin2xcosx+sin2x=1

But what next?

- #4

eumyang

Homework Helper

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The problem should be as follows:

If

[itex]\sin x + \sin^2 x + \sin^3 x = 1[/itex],

then find out the value of

[itex]\cos^6 x - 4\cos^4 x + 8\cos^2 x[/itex].

Here's a hint, and hopefully, it's not a big one:

[itex]\sin x + \sin^3 x = \cos^2 x[/itex].

Then square both sides and use the identity

[itex]\sin^2 x =1 - \cos^2 x[/itex].

You should eventually get the answer.

Mods: if this is too big of a hint, then please delete.

- #5

- 3,812

- 92

The problem should be as follows:

If

[itex]\sin x + \sin^2 x + \sin^3 x = 1[/itex],

then find out the value of

[itex]\cos^6 x - 4\cos^4 x + 8\cos^2 x[/itex].

Here's a hint, and hopefully, it's not a big one:

[itex]\sin x + \sin^3 x = \cos^2 x[/itex].

Then square both sides and use the identity

[itex]\sin^2 x =1 - \cos^2 x[/itex].

You should eventually get the answer.

Mods: if this is too big of a hint, then please delete.

You're right. I am very sorry for my foolishness. Please pardon me.

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