Proving the Sine of Sum Formula?

Question

How do you prove the sine of sum formula with the Sine Law?

Thanks

Answer 1

I found a link that may help you with your trig question.

Go to:

http://mathforum.org/library/drmath/view/54076.html

Guido

Answer 2

There are many ways to do this. The one I like best is to take euler's formula:

e^(ix)=cos x + i sin x

If z is a complex number a+bi, let im(z)=b (i.e. im(z) is the imaginary component of z). Thus:

sin x = im(e^(ix))

So to find sin (x+y):

sin (x+y)
im (e^(i(x+y)))
im (e^(ix) * e^(iy))
im ((cos x + i sin x) * (cos y + i sin y))
im (cos x cos y + i sin x cos y + i sin y cos x - sin x sin y)
sin x cos y + sin y cos x