Question

Преобразуйте произведение в сумму:
1. sin(a+b)sin(a-b)
2.cos(a+b)cos(a-b)

Answer 1

1. sin(a+b)*sin(a-b) = [ sin(a)*cos(b) + cos(a)*sin(b) ]*[ sin(a)*cos(b) - cos(a)*sin(b)] = sin(a)*cos(b)*sin(a)*cos(b) - sin(a)*cos(b)*cos(a)*sin(b) + cos(a)*sin(b)*sin(a)*cos(b) - cos(a)*sin(b)*cos(a)*sin(b) = sin2(a)cos2(b) - cos2(a)sin2(b)

 

2. cos(a+b)*cos(a-b) = [ cos(a)*cos(b) - sin(a)*sin(b) ]*[ cos(a)*cos(b) + sin(a)*sin(b) ] = cos2(a)*cos2(b) - sin2(a)*sin2(b)            (преобразования аналогичные первому примеру)