
Trig identity, tan(2A)
Have a question i'm having some trouble with,
Verify the identity;
(sin A + sin 3A) / (cos A + cos 3A) = tan 2A
not sure best way to go about this one,
tried using sin3A = sin(2A + A) and expanding out but didn't seem to give me anything i wanted.
Any help would be greatly appreciated.
Cheers.

Using the identities
$\displaystyle \sin(x \pm y) = \sin x \cos y \pm \sin y \sin x$
$\displaystyle \cos(x \pm y) = \cos x \cos y \mp \sin x \sin y$,
you can get
$\displaystyle \sin x + \sin y = 2\sin \left(\frac{x+y}{2}\right)\cos \left(\frac{xy}{2}\right)$
$\displaystyle \cos x + \cos y = 2\cos \left(\frac{x+y}{2}\right)\cos \left(\frac{xy}{2}\right)$.
Set $\displaystyle x=3A$ and $\displaystyle y=A.$

Ok, i can see how to finish the problem and this may seem like a stupid question but how did you get from the sin(x + y) formulae to the sinx + siny ones

So you have
sin (a + b) = sin a cos b + sin b cos a
sin (a  b) = sin a cos b  sin b cos a
Adding the two equations gives you
sin (a + b) + sin (a  b) = 2 sin a cos b.
Now set x = a + b and y = a  b, find a and b in terms of x and y, and you'll get the identity for sin x + sin y
(similar for cos x + cos y).