# Help with Trig Identity Simplification

## 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?

SammyS
Staff Emeritus
Homework Helper
Gold Member

## 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)​

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

$\displaystyle \frac{2\cos(\theta)-\cos(2\theta)}{2\cos(\theta)+\cos(2\theta)}$

how do you delete a comment, irrelevant I know. But I made an accidental post.

SammyS
Staff Emeritus