Proving the Identity: cos(2x)-cos(4x)/sin(2x)+sin(4x)=tanx | Homework Help

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In summary, the student is struggling to verify the equation: (cos(2x)-cos(4x))/(sin(2x)+sin(4x))=tanx. They have tried using various identities such as the sum/difference identities, Pythagorean identities, and double angle formulas, but have not been successful. They are now considering the sum-to-product identities and have been advised to look for identities involving cos a - cos b and sin a + sin b. The student has responded that they have already tried those identities without success and have asked for further help with their approach.
  • #1
Superstring
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Homework Statement

I'm supposed to verify this:
[tex]\frac{cos(2x)-cos(4x)}{sin(2x)+sin(4x)}=tanx[/tex]

The attempt at a solution

I reworked it every way I could think of, but it just won't work. I got desperate so I plugged it into some site and it said it was not a real identity, so I now I'm thinking maybe my teacher had a typo or something.
 
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  • #2
look up the sum to product formulas for sine and cosine. They should help.
 
  • #3
rock.freak667 said:
look up the sum to product formulas for sine and cosine. They should help.

I already know them, but I still can't figure it out.
 
  • #4
Superstring said:
I already know them, but I still can't figure it out.

Try applying them.
 
  • #5
rock.freak667 said:
Try applying them.

If you don't want to help then don't comment please.
 
  • #6
Superstring said:
If you don't want to help then don't comment please.

Am I correct to assume you did not apply them?
 
  • #7
rock.freak667 said:
Am I correct to assume you did not apply them?

No, you are not. Before I posted here I used the sum/dif identities, pythagorean identities, and double angle formulas. Everything I did resulted in a dead end.
 
  • #8
Superstring said:
No, you are not. Before I posted here I used the sum/dif identities, pythagorean identities, and double angle formulas. Everything I did resulted in a dead end.

Is it possible that you can post your work using the sum to product identities?
 
  • #9
You can factor out sin2x from the denominator. Resolve it further as 2 sinx cosx, and write the right side as sinx/cosx. Eliminate cosx (assuming it is not zero). Divide both sides by sinx, and rewrite 2(sinx)^2 as 1-cos(2x). You can see that the denominator is equal to the numerator.

ehild
 
  • #10
Superstring said:
No, you are not. Before I posted here I used the sum/dif identities, pythagorean identities, and double angle formulas. Everything I did resulted in a dead end.
You didn't use the right ones then. You need the sum-to-product identities. If you use them, the answer pops out in like two lines.

Look for identities for [tex]cos a - cos b[/tex] and [tex]sin a + sin b[/tex].

If, in fact, you used those already and didn't get anywhere, post what you did because that's where the difficulty lies.
 

FAQ: Proving the Identity: cos(2x)-cos(4x)/sin(2x)+sin(4x)=tanx | Homework Help

What is the purpose of proving the identity cos(2x)-cos(4x)/sin(2x)+sin(4x)=tanx?

The purpose of proving this identity is to show that the two sides of the equation are equal for all values of x. This helps to simplify expressions and solve more complex trigonometric equations.

How do you prove the identity cos(2x)-cos(4x)/sin(2x)+sin(4x)=tanx?

The most common method for proving trigonometric identities is through the use of algebra and trigonometric identities. This may involve manipulating one side of the equation to make it match the other side, or using trigonometric identities such as the double angle formula to simplify the expression.

What are some tips for solving trigonometric identities like cos(2x)-cos(4x)/sin(2x)+sin(4x)=tanx?

Some tips for solving trigonometric identities include breaking down the expression into simpler terms, using trigonometric identities and formulas, and paying attention to signs and factors. It is also helpful to practice and familiarize yourself with common identities and techniques.

Why is it important to understand and be able to prove trigonometric identities?

Understanding and being able to prove trigonometric identities is important because it allows for the simplification of expressions and solving of more complex equations. It also helps to develop a deeper understanding of trigonometric functions and their relationships.

Are there any common mistakes to avoid when proving trigonometric identities like cos(2x)-cos(4x)/sin(2x)+sin(4x)=tanx?

One common mistake to avoid when proving trigonometric identities is to only manipulate one side of the equation without making the same changes to the other side. It is also important to carefully apply trigonometric identities and formulas, and to check for any mistakes in algebraic manipulations.

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