# proof of trig identity

• Apr 10th 2010, 06:51 AM
sigma1
proof of trig identity
am trying to prove that $\displaystyle \frac {sin4A +sin2A}{cos4A + cos2A} = tan3A$
• Apr 10th 2010, 06:54 AM
Sudharaka
Quote:

Originally Posted by sigma1
am trying to prove that $\displaystyle \frac {sin4A +sin2A}{cos4A + cos2A} = tan3A$

Dear sigma1,

• Apr 10th 2010, 07:05 AM
sigma1
i have tried but i seem to be getting no where with this one.
• Apr 10th 2010, 07:36 AM
Sudharaka
Quote:

Originally Posted by sigma1
i have tried but i seem to be getting no where with this one.

Dear sigma1,

You can't be getting no where. Now use, $\displaystyle sinA+sinB=2sin\frac{A+B}{2}cos\frac{A-B}{2}$ for the numerator, and $\displaystyle cosA+cosB=2cos\frac{A+B}{2}cos\frac{A-B}{2}$ for the denominator.

• Apr 10th 2010, 07:53 AM
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,