Setting functions equal to each other to cancel

  • Thread starter getty102
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In summary, to set functions equal to each other to cancel, you need to identify the two functions, solve for the variable in each function, and then set the equations equal to each other. This technique is useful in algebra, especially when solving systems of equations, as it simplifies the problem by eliminating one variable. However, it only works when the functions have the same variable and coefficient. It is also possible to use this technique with more than two functions, but it may become more complex. Additionally, there are other methods to solve systems of equations, such as substitution, elimination, and graphing.
  • #1
getty102
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Homework Statement



sin(3x)=3sin(x)

Homework Equations





The Attempt at a Solution



How do you solve this for x?
 
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  • #2
What identity can you replace sin(3x) with? (Hint: you want to write everything in terms of sinx)
 
  • #3
Well I came up with;
(1+2cos(2x))sinx=3sinx

but that didn't work either
 
  • #4
getty102 said:
Well I came up with;
(1+2cos(2x))sinx=3sinx

but that didn't work either


and you can replace cos(2x) by?
 

1. How do you set functions equal to each other to cancel?

To set functions equal to each other to cancel, you first need to identify the two functions that you want to set equal. Then, you need to solve for the variable in each function. Finally, you can set the two equations equal to each other and solve for the variable, which will result in the functions canceling each other out.

2. Why would you want to set functions equal to each other to cancel?

Setting functions equal to each other to cancel is a useful technique in algebra, especially when solving systems of equations. It allows you to eliminate one variable and solve for the other, making the problem simpler and easier to solve.

3. Are there any limitations to setting functions equal to each other to cancel?

Yes, there are some limitations to this technique. It only works when the two functions have the same variable and the same coefficient. If the functions have different variables or coefficients, you cannot set them equal to each other to cancel.

4. Can you use this technique with more than two functions?

Yes, you can set multiple functions equal to each other to cancel. However, it will require more steps and may become more complex. It is recommended to use this technique with only two functions at a time.

5. Is setting functions equal to each other to cancel the only way to solve a system of equations?

No, there are other methods to solve systems of equations, such as substitution, elimination, and graphing. However, setting functions equal to each other to cancel is a quick and efficient method, especially when the equations are already in a simplified form.

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