How to factor cos22X + cos2X = 0

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To factor the equation cos22X + cos2X = 0, recognize that cos22X can be expressed as (cos2X)². This allows for factoring out cos2X, leading to the equation cos2X(cos2X + 1) = 0. The solutions include cos2X = 0 and cos2X + 1 = 0. Substituting cos2X with y simplifies the problem to y² + y = 0, which factors to y(y + 1) = 0. The discussion emphasizes both factoring and solving the equation.
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How do I factor this?

cos22X + cos2X = 0
 
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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:
 


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
 

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