Verify that cos(2x)-cos(4x)/sin(2x)+sin(4x)=tanx

[Superstring]

Homework Statement

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

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.

 

[rock.freak667]

look up the sum to product formulas for sine and cosine. They should help.

 

[Superstring]

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.

 

[rock.freak667]

I already know them, but I still can't figure it out.

Try applying them.

 

[Superstring]

Try applying them.

If you don't want to help then don't comment please.

 

[rock.freak667]

If you don't want to help then don't comment please.

Am I correct to assume you did not apply them?

 

[Superstring]

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.

 

[rock.freak667]

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?

 

[ehild]

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

 

[vela]

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 $$cos a - cos b$$ and $$sin a + sin b$$.

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