1. cos(x-y)-sin(x)sin(y)
Разложим выражение cos(x-y) по формуле cos(t-s)=cos(t)cos(s) + sin(t)sin(s)
Получаем cos(x-y)-sin(x)sin(y) = cos(x)cos(y) + sin(x)sin(y) - sin(x)sin(y)
Сокращаем противоположные выражения и получаем
cos(x-y)-sin(x)sin(y) = cos(x)cos(y) + sin(x)sin(y) - sin(x)sin(y) = cos(x)cos(y)
2. sin(a)cos(b)-sin(a-b) = sin(a)cos(b) - sin(a)cos(b) - cos(a)sin(b)=- cos(a)sin(b)
3. cos(a)cos(b)-cos(a-b) = cos(a)cos(b) - cos(a)cos(b) - sin(a)sin(b) = - sin(a)sin(b)
