Question

I am asked to use a sum-to-product identity to find the ID for cosx-cos7x. i came up with 2sin4xsin3x. is that correct?

Answer 1

sorry NEGATIVE in front, as in - 2sin4xsin3x

Answer 2

The identity you want is:
\[\cos(x)-\cos(y)=-2\sin(\frac{x+y}{2})\sin(\frac{x-y}{2})\]
In this case: x=x and y=7x.
\[\cos(x)-\cos(7x)=-2\sin(\frac{x+7x}{2})\sin(\frac{x-7x}{2})=-2\sin(4x)\sin(-3x)\]

Answer 3

Using the fact that sine is odd you can say:
\[\sin(-3x)=-\sin(3x)\]
Making it:
\[2\sin(4x)\sin(3x)\]
As you have.

Answer 4

why does my book not have the (-) in front of the 2 at the beginning of the identity?

Answer 5

i am looking at another sheet online (attached) that does indeed have the - you put in, but why doesn't my book?

Answer 6

I have no idea.

Answer 7

crazay