Prove (cosx+cos4x+cos7x) / (sinx+sin4x+sin7x) = cot4x

[stefanie_parker24]

I need help proving this identity. Once I get started on it, I end up with a rediculously long and complicated problem. There has to be an abreviated version of what I'm doing.

(cos x + cos 4x + cos 7x)/(sin x + sin 4x + sin 7x) = cot 4x

The way that I have been working it is to break down both the numerator and the denominator using the double angle identities. But by the time I've got them all broken down, I have so much that I've mananged to confuse myself. If anyone could help me break this down in a more simple manner I would really appreciate it.

 

[royhaas]

Start with $\displaystyle u = \frac{u+v}{2} + \frac{u-v}{2}, v = \frac{u+v}{2} - \frac{(u-v)}{2}$. Now use the sum formulas, e.g., $\displaystyle \cos(u)+\cos(v) = ...$ to develop products.