Trig question

  • Thread starter Saitama
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  • #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? :confused:
I don't find any way to convert them to cos 6x or cos 4x.
 

Answers and Replies

  • #2
SammyS
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Try using [itex]\displaystyle \sin \theta + \sin \varphi = 2 \sin\left( \frac{\theta + \varphi}{2} \right) \cos\left( \frac{\theta - \varphi}{2} \right)[/itex] to combine sin(x) + sin(3x) .

-- Just a possibility.
 
  • #3
3,812
92
Try using [itex]\displaystyle \sin \theta + \sin \varphi = 2 \sin\left( \frac{\theta + \varphi}{2} \right) \cos\left( \frac{\theta - \varphi}{2} \right)[/itex] to combine sin(x) + sin(3x) .

-- Just a possibility.

Using this identity i get:-
2sin2xcosx+sin2x=1

But what next?
 
  • #4
eumyang
Homework Helper
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I don't think the problem was copied correctly. I've seen this problem before. The numbers in front of the x's are supposed to be exponents, not multiples of angles.

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:
Rewrite as
[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
I don't think the problem was copied correctly. I've seen this problem before. The numbers in front of the x's are supposed to be exponents, not multiples of angles.

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:
Rewrite as
[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.:frown:
 

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