am trying to prove that $\displaystyle \frac {sin4A +sin2A}{cos4A + cos2A} = tan3A$

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- Apr 10th 2010, 06:51 AMsigma1proof of trig identity
am trying to prove that $\displaystyle \frac {sin4A +sin2A}{cos4A + cos2A} = tan3A$

- Apr 10th 2010, 06:54 AMSudharaka
- Apr 10th 2010, 07:05 AMsigma1
i have tried but i seem to be getting no where with this one.

- Apr 10th 2010, 07:36 AMSudharaka
- Apr 10th 2010, 07:53 AMArchie Meade
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.