SOLUTION: Express sin(x)sin(x-y) as a difference of two cosines.

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Question 1048795: Express sin(x)sin(x-y) as a difference of two cosines.
Answer by Edwin McCravy(20067) About Me  (Show Source):
You can put this solution on YOUR website!
    
cos%28A-B%29%22%22=%22%22cos%28A%29cos%28B%29%2Bsin%28A%29sin%28B%29
cos%28A%2BB%29%22%22=%22%22cos%28A%29cos%28B%29-sin%28A%29sin%28B%29

Subtract the 2nd equation from the 1st:

cos%28A-B%29+-+cos%28A%2BB%29%22%22=%22%222sin%28A%29sin%28B%29

Multiply both sides by 1/2

expr%281%2F2%29%28cos%28A-B%29%5E%22%22+-+cos%28A%2BB%29%29%22%22=%22%22sin%28A%29sin%28B%29

sin%28A%29sin%28B%29%22%22=%22%22expr%281%2F2%29%28cos%28A-B%29%5E%22%22+-+cos%28A%2BB%29%29

Let A = x and B = x-y

sin%28x%29sin%28x-y%29%22%22=%22%22

sin%28x%29sin%28x-y%29%22%22=%22%22expr%281%2F2%29%28cos%28x-x%2By%5E%22%22%29%5E%22%22+-+cos%28x%2Bx-y%5E%22%22%29%29

sin%28x%29sin%28x-y%29%22%22=%22%22expr%281%2F2%29%28cos%28y%5E%22%22%29%5E%22%22+-+cos%282x-y%5E%22%22%29%29

That's ONE-HALF the difference of two cosines, which may be what
you want.  If not let me know in the thank-you note form below,
and I'll try to get rid of the ONE-HALF.

Edwin