How to factor cos22X + cos2X = 0

  • Thread starter Aceradonia
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In summary, the first step in factoring cos22X + cos2X = 0 is to factor out the common factor of cos2X, which results in cos2X(cos20 + 1) = 0. This equation can be further simplified by using the identity cos2X = 2cos2X - 1, giving 2cos2X(cos2X - 1) = 0. To solve for the values of X, you need to set each factor equal to 0 and solve for X, resulting in X = π/4 and X = 3π/4 as solutions. However, this equation cannot be factored using the quadratic formula and needs to be solved using trigonometric
  • #1
Aceradonia
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How do I factor this?

cos22X + cos2X = 0
 
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  • #2
Welcome to PF!

Hi Aceradonia ! Welcome to PF! :smile:
Aceradonia said:
How do I factor this?

cos22X + cos2X = 0

Well, cos22X is the same as (cos2X)2,

so you can factor out a cos2X. :smile:

hmm … did you mean solve, rather than factor? … then cos2x = 0 is one set of solutions, and the other is … ? :wink:
 
  • #3


You will easy realize it, maybe (not necessarily) if you substitute for cos2X=y, you will come up with y2+y=0. Out of there: y(y+1)=0
 

1. What is the first step in factoring cos22X + cos2X = 0?

The first step in factoring this equation is to factor out the common factor of cos2X. This will leave you with cos2X(cos20 + 1) = 0.

2. Can you simplify cos22X + cos2X = 0 further?

Yes, you can simplify the equation further by using the identity cos2X = 2cos2X - 1. This will give you 2cos2X(cos2X - 1) = 0.

3. How do you solve for the values of X in this equation?

To solve for the values of X, you need to set each factor equal to 0 and solve for X. In this case, cos2X = 0 and cos2X - 1 = 0. This will give you X = π/4 and X = 3π/4 as the solutions.

4. Can this equation be factored using the quadratic formula?

No, this equation cannot be factored using the quadratic formula because it is not in the form of ax² + bx + c = 0. It is a trigonometric equation and needs to be solved using trigonometric identities.

5. How can factoring this equation be useful in solving trigonometric equations?

Factoring can be useful in solving trigonometric equations as it helps simplify the original equation and allows for easier identification of possible solutions. It can also help in applying trigonometric identities to further simplify the equation and solve for the variables.

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