Help with Trig Identity Simplification

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Homework Statement



Simplify (2cos2x-cos4x)/(2cos2x+cos4x)

The Attempt at a Solution



I let θ = 2x

(2cosθ-cos2θ)/2cosθ+cos2θ)

Since cos2θ= 1-2cos^2

(2cosθ-(1-2cos^2)/2cosθ+1-2cos^2


But I get lost when applying it and can't get beyond this, Do i have to use the quadratic formula?
 

Answers and Replies

  • #2
SammyS
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Homework Statement



Simplify (2cos2x-cos4x)/(2cos2x+cos4x)

The Attempt at a Solution



I let θ = 2x

(2cosθ-cos2θ)/(2cosθ+cos2θ)

Since cos2θ= 1-2cos^2θ

(2cosθ-(1-2cos^2θ)/(2cosθ+1-2cos^2θ)

But I get lost when applying it and can't get beyond this, Do I have to use the quadratic formula?
How can you use the quadratic formula without an equation? (Actually it is possible to do that.)

You dropped some θs and some important parentheses.

Your identity for cos(2θ) is incorrect.
cos(2θ) = 2cos2(θ) - 1
= cos2(θ) - sin2(θ)

= 1 - 2sin2(θ)​
Take your pick.​

Writing your expression with LaTeX after substituting θ for 2x gives:

[itex]\displaystyle \frac{2\cos(\theta)-\cos(2\theta)}{2\cos(\theta)+\cos(2\theta)}[/itex]
 
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how do you delete a comment, irrelevant I know. But I made an accidental post.
 
  • #4
SammyS
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how do you delete a comment, irrelevant I know. But I made an accidental post.
Click the edit.

Choose the delete message box.

Then there's another place that shows up. Click that to finally delete the post.
 

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