1. ## sin(u)cos(v) != cos(v)sin(u)??

I need help understanding these trig identities:

$\displaystyle sin(a)cos(b) = (sin(a+b) + sin(a-b))/2$

Where I see this identity I also see it followed up by this identity:

$\displaystyle cos(b)sin(a) = (sin(b+a) - sin(b-a))/2$

Huh? I recall that:

$\displaystyle sin(-u) = -sin(u)$

So cos(b)sin(a) becomes:

$\displaystyle cos(b)sin(a) = (sin(b+a) + sin(a-b))/2$

Right? but this is NOT equal to the sin(a)cos(b) equation above. Shouldn't it be?

I know that xy=yx so shouldn't cos(b)sin(a) = sin(a)cos(b)?

Where is my logic flawed...

I need help understanding these trig identities:

$\displaystyle sin(a)cos(b) = (sin(a+b) + sin(a-b))/2$

Where I see this identity I also see it followed up by this identity:

$\displaystyle cos(b)sin(a) = (sin(b+a) - sin(b-a))/2$

Huh? I recall that:

$\displaystyle sin(-u) = -sin(u)$

So cos(b)sin(a) becomes:

$\displaystyle cos(b)sin(a) = (sin(b+a) + sin(a-b))/2$

Right? but this is NOT equal to the sin(a)cos(b) equation above. Shouldn't it be?

I know that xy=yx so shouldn't cos(b)sin(a) = sin(a)cos(b)?

Where is my logic flawed...
i don't see your problem. if you make the change you spoke about in the second equation, you get the first. if you make it in the first, you get the second. they are equal.

3. I just went through the equality. I apologize for wasting your time, and I am a little embarrassed.

I just went through the equality. I apologize for wasting your time, and I am a little embarrassed.
haha, don't worry about it. our little secret