Verifying an Identity

1. Jan 7, 2010

Superstring

The problem statement, all variables and given/known data

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.

2. Jan 7, 2010

rock.freak667

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

3. Jan 7, 2010

Superstring

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

4. Jan 7, 2010

rock.freak667

Try applying them.

5. Jan 7, 2010

Superstring

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

6. Jan 7, 2010

rock.freak667

Am I correct to assume you did not apply them?

7. Jan 7, 2010

Superstring

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. Jan 7, 2010

rock.freak667

Is it possible that you can post your work using the sum to product identities?

9. Jan 7, 2010

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

10. Jan 8, 2010

vela

Staff Emeritus
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.