Упростите выражения cos (t - s) – sin t sin s; sin (α - β) + cos α sin β ; ) sin α cos β...

Решите задачу:

$1) cos(t - s) - sin(t)\cdot sin(s) = cos(t)\cdot cos(s) + sin(t)\cdot sin(s) - \\ - sin(t)\cdot sin(s) = cos(t)\cdot cos(s)$

$2) sin(\alpha - \beta) + cos(\alpha)\cdot sin(\beta) = sin(\alpha)\cdot cos(\beta) - \\ - sin(\beta) \cdot cos(\alpha) + cos(\alpha)\cdot sin(\beta) = sin(\alpha)\cdot cos(\beta)$

$5)sin(\alpha)\cdot cos(\beta) - sin(\alpha - \beta) = sin(\beta)\cdot cos(\alpha)$

$4) cos(x)\cdot cos(y) - cos(x - y) = - sin(x)\cdot sin(y)$