sin(x+y) + sin(x-y) = 2sinxcosy

I did it until I got (sinxcosy)^2 - (cosxsiny)^2 and I got stuck.

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sin(x + y) = sin(x)cos(y) + cos(x)sin(y) sin(x - y) = sin(x)cos(y) - cos(x)sin(y) So we get: sin(x + y) + sin(x - y) = sin(x)cos(y) + cos(x)sin(y) + sin(x)cos(y) - cos(x)sin(y) = [sin(x)cos(y) + sin(x)cos(y)] + [cos(x)sin(y) - cos(x)sin(y)] = 2sin(x)cos(y)

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