# Homework Help: Trying to prove a trig identity

1. Aug 6, 2013

### Appleton

1. The problem statement, all variables and given/known data
prove that (sinA +sin3A + sin5A)/(cosA + cos3A + cos5A) = tan3A

2. Relevant equations
sinP + sinQ = 2sin((P+Q)/2)cos((P-Q)/2)
cosP + cosQ = 2cos((P+Q)/2)cos((P-Q)/2)

3. The attempt at a solution
(sin3A + sinA) + sin5A = 2sin2AcosA + 2sin((5/2)A)cos((5/2)A)
(cos3A + cosA) + cos5A = 2cos2AcosA + 2cos((5/2)A + 45)cos((5/2)A - 45)
It started to feel like a bit of a cul de sac at this point so I tried pursuing variations on this theme by starting with (sin5A + sin3A) + sinA etc, but these seemed just as fruitless.

2. Aug 6, 2013

### voko

Because the right hand side is a function of 3A, it could be useful to combine A and 5A on the left hand side.

3. Aug 6, 2013

### verty

I haven't checked what Voko suggested but you could also try this: let p = 3A, q = 2A.

4. Aug 6, 2013

### Saitama

voko's suggestion is nice. I was able to solve the problem without pen and paper using his hint. I would suggest Appleton to try that. :)

5. Aug 7, 2013

### Appleton

Thanks for all your suggestions, voko's suggestion led me to the proof, however, I'm still unable to eliminate the pen and paper.