Re: sum of three sines

In article
<1c256be8cff4e508d7e8fb05892ad8e3.35661@xxxxxxxxxxxxxxxxxxx>,
David
Macmanus <macmanus@xxxxxxxxxx> wrote:

I've been trying to find the three sum equivalent of
sinA + sinB = 2sin(A+B/2)cos(A-B/2),
i.e. what is
sinA + sinB + sinC = ??
I've looked on the web but can't seem to find it.
Does anyone know of a web-site or have the answer handy?
Thanks,
David.

Well, for sin(a) + sin(b), Maple does this:

convert(%,exp);expand(%);factor(%);

1 / 1 \ 1 / 1 \
-- I |exp(I a) - --------| - - I |exp(I b) - --------|
2 \ exp(I a)/ 2 \ exp(I b)/

1 1
- I - I
1 2 1 2
-- I exp(I a) + -------- - - I exp(I b) + --------
2 exp(I a) 2 exp(I b)

1
- I (exp(I b) + exp(I a)) (exp(I b) exp(I a) - 1)
2
- -------------------------------------------------
exp(I a) exp(I b)

and now each of the two factors in the numedrator can be recognized as
an exp times a cos or sin.

But for sin(a) + sin(b) + sin(c) we get

-1/2*I*((exp(I*a))^2*exp(I*b)*exp(I*c)-exp(I*b)*exp(I*c)+(exp(I*b))^2*ex
p(I*a)*exp(I*c)-exp(I*a)*exp(I*c)+(exp(I*c))^2*exp(I*a)*exp(I*b)-exp(I*a)
*exp(I*b))/(exp(I*a)*exp(I*b)*exp(I*c))

and Maple does not factor that. I = sqrt(-1) .

.