Question

Trig Identities Question: say we have sin(x+deltax) = sinx*cosdeltax + cosx*sindeltax

and we want to introduce -sinx on both sides.

So, how can I put -sinx on the left, and a -1 on the right like this:

sin(x+deltax) - sinx = sinx*(cosdeltax-1) + cosx*sindeltax

Professor Strang is doing this in a video lecture, and I want to understand what the basis for this is. Can you help me understand this?

Answer 1

I'm going to use y instead of deltax to save time.


sin(x+y) = sin(x)*cos(y) + cos(x)*sin(y)



Now subtract sin(x) from both sides

sin(x+y) - sin(x) = sin(x)*cos(y) + cos(x)*sin(y) - sin(x)



Group like terms and factor

sin(x+y) - sin(x) = (sin(x)*cos(y) - sin(x)) + cos(x)*sin(y)


sin(x+y) - sin(x) = sin(x)*(cos(y) - 1) + cos(x)*sin(y)



Now if you want, you can replace y with deltax again to get


sin(x+deltax) - sin(x) = sin(x)*(cos(deltax) - 1) + cos(x)*sin(deltax)

Answer 2

you are thinking way too hard. it is not trig, it is algebra

Answer 3

what jimthompson wrote. it is not a trig identity at all

Answer 4

Thanks, I seem to have lost my mind due to cos and sin being on the scene.