Question

упростите выражения
1) cos(x-y)-sinxsiny
2) sinacosb-sin(a-b)
3) cosacosb-cos(a-b)

Answer 1

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)