Express the sum/difference as a product

Question

1) sin(6x)+sin(2x)

2)cos(3x/2)+cos(x/2)

Answer 1

sin(a) cos(b) = 1/2 ( sin(a+b) + sin(a-b))

then

2 sin(a) cos(b) = ( sin(a+b) + sin(a-b))

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a=4x and b=2x

then 2 sin(4x) cos(2x) = sin(6x) + sin(2x) for #1

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LIkewise, cos(a) cos(b) = 1/2 ( (cos(a+b) + cos(a-b))

2 cos(a) cos(b) = cos(a+b) + cos(a-b)

The product you want is then 2 cos(pi) cos((1/2)pi)