am trying to prove that $\displaystyle \frac {sin4A +sin2A}{cos4A + cos2A} = tan3A$
Hi sigma1,
if it looks confusing with "A" in both,
you can rewrite it as
$\displaystyle SinX+SinY=2Sin\left(\frac{X+Y}{2}\right)Cos\left(\ frac{X-Y}{2}\right)$
where X=4A, Y=2A
and
$\displaystyle CosX+CosY=2Cos\left(\frac{X+Y}{2}\right)Cos\left(\ frac{X-Y}{2}\right)$
When you work this out, you will have cancellation of terms in your fraction,
leading to the result.