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)
gives:
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)]
who found trigonometry?