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I arrived at this sum or trigonometric functions that I need to turn into a product in order to continue the exercise. How do I do that?

$$\sin{x}\cos{(x+y)} -\cos{x}\sin{(x+y)}$$

I know of the identities of $\cos{(a \pm b)}$ and $\sin{(a \pm b)}$, but I can't figure the solution out.

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up vote 3 down vote accepted

Letting $a=x$ and $b=x+y$, you have $$\sin a\cos b-\cos a\sin b=\sin(a-b).$$

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