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Solve Sin6x+sin4x

  • #1

Homework Statement



[tex]sin6x+sin4x=0[/tex]

Homework Equations



[tex]sinx=2sin\frac{x}{2}cos\frac{x}{2}[/tex]

[tex]sin2x=2sinxcosx[/tex]

[tex]cos2x=cos^2x-sin^x[/tex]

The Attempt at a Solution



[tex]2sin3xcos3x+2sin2xcos2x=0[/tex]

[tex]sin3xcos3x+sin2xcos2x=0[/tex]

What shall I do next?
 

Answers and Replies

  • #2
Defennder
Homework Helper
2,591
5
What exactly are you suppose to do? What is the question?

EDIT: Is it to solve for x?
 
  • #3
Yes. I need to find x.
 
  • #4
Ohh... Can I solve it like this:

[tex]sin6x=-sin4x[/tex]

[tex]sin6x=sin(-4x)[/tex]

[tex]6x=-4x+2k\pi[/tex]

[tex]10x=2k\pi[/tex]

[tex]x=\frac{k\pi}{5}[/tex]

??
 
  • #5
Defennder
Homework Helper
2,591
5
That is partially correct. But you're missing out on other possible values of x. [tex]x=\frac{\pi}{2} [/tex] also satisfies the equation but it's not expressible in your answer.

Use this trigo identity:
[tex]2sin(Ax)cos(Bx) = sin((A-B)x) + sin((A+B)x)[/tex]
 
  • #6
Yes I forgot.

[tex]6x=\pi+4x+2k\pi[/tex]

[tex]x=\frac{\pi}{2}+k\pi[/tex]
 
  • #7
Defennder
Homework Helper
2,591
5
Where did pi in your first equation come from?
 
  • #8
Remember this:

x=arcsinx+2kpi

x=pi - arcsinx + 2kpi

?
 

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