expres the following as sums and differences of sines or cosines
cos8t * sin2t

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

replacing by by -b and using that
cos(-b)= cos(b)
sin(-b)= -sin(b)


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

Add the two equations:

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

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

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