How do you solve for cos2x = 2 cosx sinx?

  • Context: High School 
  • Thread starter Thread starter Maria
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Discussion Overview

The discussion revolves around solving the equation cos(2x) = 2cos(x)sin(x), exploring various methods and transformations to find the values of x that satisfy this equation. Participants engage in mathematical reasoning, providing insights into trigonometric identities and the implications of the equation.

Discussion Character

  • Mathematical reasoning
  • Technical explanation
  • Homework-related
  • Exploratory

Main Points Raised

  • Some participants suggest using the identity 2cos(x)sin(x) = sin(2x) to simplify the equation.
  • There is a distinction made between the original equation and the identity, with some participants noting that cos(2x) = 2cos(x)sin(x) is not an identity.
  • One participant expresses uncertainty about the transformation leading to cos(2x) = sin(2x) and seeks clarification.
  • Participants discuss the implications of solving tan(2x) = 1, leading to multiple angles being derived.
  • There is a focus on finding specific angles within the range of 0 to 360 degrees, with various values of n being considered.
  • Some participants clarify the process of deriving angles from the tangent function and the reasoning behind obtaining four distinct solutions instead of two.

Areas of Agreement / Disagreement

Participants generally agree on the methods to approach the problem, but there are varying interpretations of the transformations and the implications of the identities used. The discussion remains unresolved regarding the clarity of certain steps and the reasoning behind the number of solutions.

Contextual Notes

Some participants express uncertainty about the validity of dividing by cos(2x) and the implications of doing so. There are also discussions about the preferred format for presenting solutions, indicating a dependence on individual instructor preferences.

Who May Find This Useful

Students studying trigonometric equations, individuals seeking to understand the application of trigonometric identities, and those interested in problem-solving techniques in mathematics may find this discussion beneficial.

  • #31
I have on stupid question left:
Why do I get 4 angles instead og just 2?
Is it because tan =1?
 
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  • #32
You get 4 distinct angles because you must solve tan(2x)=1 rather than tan(x)=1
If for example, you were to solve tan(4x)=1, you would have even more distinct solutions
(You could work out how many for yourself)
 
  • #33
thanks a lot for answering all my stupid questions...
 

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